The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

6.0 cm
6.1 cm
8.4 cm
8.5 cm

Answers

Answer 1

Answer:

6.1 cm

Step-by-step explanation:

it depends on what your teacher told you and wants to see.

because, theoretically, it would be 6.0 cm. but that would render the whole triangle into a flat line, as the 2 equal sides together (2×6 = 12) would be exactly as long as the baseline (12) of the triangle.

which is again a theoretically possible construct (counting as extreme triangle).

but it is more likely that your teacher wants the definition applied that for each combination of 2 sides this combination has to be larger (and not larger or equal) than the third side.

so, the 2 equal sides have to be larger than 6 cm.

the smallest number in your answer options to fit that criteria is 6.1 cm

just FYI - your teacher was not very precise in the phrasing, because there are many numbers smaller than 6.1 that would still be correct.

like 6.01, or 6.005, ...

Answer 2

Rounded to the nearest tenth, the smallest possible length is 6.1 cm.Thus, the answer is B) 6.1 cm.

In an acute isosceles triangle, the longest side is opposite the largest angle. Since the triangle is isosceles, the two congruent sides are equal in length.

In an acute triangle, the largest angle is less than 90 degrees. In an isosceles triangle, the two base angles are congruent. Therefore, each base angle must be less than 45 degrees.

Now, let's apply the triangle inequality theorem to determine the smallest possible length of one of the congruent sides. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the longest side is 12 centimeters. Let's assume each of the congruent sides has a length of x centimeters.

Based on the triangle inequality theorem, we have the following inequality:

2x > 12

To find the smallest possible length, we divide both sides of the inequality by 2:

x > 6

Therefore, the smallest possible length of one of the two congruent sides is greater than 6 centimeters.

Rounded to the nearest tenth, the smallest possible length is 6.1 cm.

Thus, the answer is B) 6.1 cm.

To know more about  congruent sides , here

https://brainly.com/question/29789999

#SPJ2


Related Questions

Find the lower quartile for the data. {66, 70, 75, 72, 67, 68, 65, 69, 68}

A. 66.5
B. 69
C. 69.5
D. 70

Answers

Answer:

66.5 is the answer thanks

How to make 10000 by only using number 8, No matter what the operation is​
BRAINLIEST will be marked

Answers

Here is the answer

[tex]\\ \sf\longmapsto 8888+888+88+88+8+8+8+8+8+8[/tex]

Similar Question .

Write 1000 using 8

Answer:-

888+88+8+8+8

Answer:

One of the options comes from this:

10000/8 = 1250

It means 10000 contains 1250 of 8's:

1250 = 1111 + 139 = 1111 + 111 + 28 = 1111 + 111 + 11 + 11 + 6

The 8's to make 10000 are:

10000 = 8888 + 888 + 88 + 88 + 8 + 8 + 8 + 8 + 8 + 8

(2x + 5) + (x + 4) =

Answers

Answer:

3x + 9

Step-by-step explanation:

(2x + 5) + (x + 4)

Distribute the + to all numbers/variables

2x + 5 + x + 4

Combine like terms:

2x + 5 + x + 4

3x + 5 + 4

3x + 9

Hope this helped.

Solve for x in 5x²-42-1=0, using factorization method

Answers

Answer:

x=2.932576,−2.932576

Determine whether the given value is a statistic or a parameter. A study was conducted of all 1575 workers in a certain state.

Answers

Answer:

Step-by-step explanation:

Which compound inequality could this graph be the solution

Answers

Answer:

A. 3x+14≥ 2 or 1-x ≥-5

Step-by-step explanation:

the solutions should be x≥ -4 or x ≤6

and the right answer is :

3x + 14≥ 2

3x ≥ -12

x≥ -4

1-x ≥ -5

-x ≥ -6

x ≤ 6

A. 3x+14≥ 2 or 1-x ≥-5

help me do this please!

Answers

Answer:

m<ABD = 37°

m<DBC = 58°

Step-by-step explanation:

m<ABD + m<DBC = m<ABC

2x + 23 + 9x — 5 = 95

11x + 18 = 95

     -18     -18

--------------------

11x = 77

/11      /11

---------------------

x = 7

Now, plug this into the equation for m<ABD and m<DBC to find their values.

m<ABD = 2x + 23

= 2(7) + 23

= 14 + 23

= 37

m<DBC = 9x — 5

= 9(7) — 5

= 63 – 5

= 58

Now, check to see if our values are right or not.

2x + 23 + 9x — 5 = 95

2(7) + 23 + 9(7) — 5 = 95

14 + 23 + 63 – 5 = 95

100 – 5 = 95

95 = 95 CORRECT

HELPPPPPP!!!!!!!!!!!!!!

Answers

Answer:

7

Step-by-step explanation:

no need to panic !

it is actually totally easy.

we have the complete, big angle at U (imagine you turn VU around U into UT) = 178 degrees.

VT is almost a straight line (then that angle would be 180 degrees). but only almost ...

anyway, the other 2 angles are just parts of the big angle, and we see that together they sum up to the big angle, as there is no other space for a part of the big angle left.

so

(14x - 11) + (12x + 7) = 178

14x - 11 + 12x + 7 = 178

26x - 4 = 178

26x = 182

x = 7

Solve for x and find the value of the unknown angle measures.
1. x=
2. m=
3. n=
4. p=

Answers

Answer:

x=20°

m=50°

n=68°

p=50°

Step-by-step explanation:

Here,we know that,

i)n=68°[being vertically opposite angle]

ii)p+62°+n=180°[being straight angle]

or, p+62°+68°=180°

or, p+130°=180°

or, p=180°-130°

thus, p=50°

iii) m=p[being vertically opposite angle]

thus, m=50°

iv)(2+3x)°=62°[being vertically opposite angle]

or, 3x°=62°-2°

or, 3x°=60°

or, x=60°÷3°

thus, x=20°

Hence, the value of x=20°, m=50°, n=68° and p=50°.

union and intersection of sets

Answers

Answer:

The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B. The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.

Answer:

Union

The union of a set A with a B is the set of elements that are in either set A or B. The union is denoted as A∪B. For example, if A is the set {♢,♡,♣,♠} and B is the set {△,♡,♠}, then A∪B={♢,♡,♣,♠,△}.

Intersection

Intersection of two given sets is the largest set which contains all the elements that are common to both the sets. To find the intersection of two given sets A and B is a set which consists of all the elements which are common to both A and B. The symbol for denoting intersection of sets is '∩'.

find the area of point b??

Answers

Answer:

78.5 in^2

or

506.7 cm^2

Step-by-step explanation:

r = 5 in = 12.7 cm

Area of circle

[tex] = \pi \times {r}^{2} [/tex]

Estimate and solve:
67+35
89-54

Answers

Answer:

32

35

Step-by-step explanation:

hope this helps :D

Answer:

Estimate and solve:

67+35

89−54

Add 67 and 35.

102

Subtract 54 from 89.

35

List all of the solutions.

67+35=102

89−54=35

Step-by-step explanation:

19. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is (a) 20 (b) 23 (c) 169 (d) None of these​

Answers

Answer:

B

Step-by-step explanation:

Let the two numbers be a and b.

The product of the two is 120 and their sum of their squares is 289. In other words:

[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]

And we want to find the sum of the two numbers.

We can use the perfect square trinomial. Recall that:

[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]

From the first equation, multiply by two:

[tex]2ab = 240[/tex]

Add the two equations together:

[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]

Simplify and rewrite:

[tex]a^2+2ab+b^2 = 529[/tex]

Factor using the perfect square trinomial pattern:

[tex](a+b)^2 = 529[/tex]

And take the square root of both sides:

[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]

Hence, the sum of the two numbers is 23 or -23.

In conclusion, our answer is B.

Find ef if e (1,-2) and f (7,6)

Answers

y-y1=a(x-x1)
a=(y2-y1)/(x2-x1)
a= (6-(-2))/(7-1)
a=8/6
a=4/3
y-6=4/3(x-7)
y-6=4/3x-28/3
y=4/3x-28/3+6
y=4/3x-10/3 >>ef

A student's cost for last semester at her community college was $2800. She spent $308 of that on books. What percent of last semester's college costs was spent on
books?
% of last semester's college costs was spent on books.

Answers

You want to divide the cost of the books by the total costs.

308/2800 = 0.11

You then need to convert 0.11 to a percent: 0.11 = 11%

Therefore, 11% of her costs last semester were spent on books.

That’s too much!

Find the surface area of a cylinder with a base radius of 2 in and a height of 5 in

Answers

Answer:

[tex]r = 2 \\ h = 5 \\ a = 2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi \times 2 \times 5 + 2\pi {2}^{2} \\ = 20\pi + 8\pi \\ = 28\pi \\ = 28 \times 3.14 \\ = 87.92 {unit}^{2} \\ thank \: you[/tex]

Help pls i’ll also rate brainliest

Answers

Answer:b

Step-by-step explanation:

Combine Like Terms
4. Which expression is equivalent to -9 + 8y + 12 - (-2y) + 1 ?
14y
10y
4+6y
10y+4

Answers

Answer:

10y + 4

Step-by-step explanation:

-9 + 8y + 12 - (-2y) + 1

-9 + 8y + 12 + 2y + 1

8y + 2y - 9 + 12 + 1

10y + 4

Help please! Find the converse

Answers

Answer:

Step-by-step explanation:

The  converse of ~q  =>  ~p  is  ~p  =>  ~q.


The radius of a circle is 4.6 millimeters. Find the diameter.

Answers

Hi :)

Radius is half the diameter

4.6 mm (2) = 9.2 mm

The diameter of the circle is 9.2 mm.

¾ + ½ =
Plz help me
I neeeeed help

Answers

1.25 would be the answer

answer

1.25

Step-by-step explanation:

[tex] \frac{3}{4} + \frac{1}{2} [/tex]

[tex] \frac{3 \times 1 + 1 \times 2}{4} [/tex]

[tex] \frac{3 + 2}{4} [/tex]

[tex] \frac{5}{4} [/tex]

[tex]1.25[/tex]

I hope this will help you..please mark my answer as BRAINLIEST....

I need help with this homework
2x^2+ 7x+ 5= 0

Answers

Answer:

x = -1 or/and -5/2

Step-by-step explanation:

:)

I am a prime number. I am two digits.
The sum of my digits is 8.
My tens digit is 6 less than my ones digit.

Answers

Answer:

17

Step-by-step explanation:

17 is a prime number17 has two digitsThe digits in 17, 1 and 7, add up to 8The tens digit is 6 less than the ones digit place.

Answer: 17

Step-by-step explanation:

1+7=8

The ten digit is (1) 6 less than the one digit (7)

FIRST -CORRECT- ANSWER WILL GET BRAINLIEST!!

Find u.


A. 2√2

B. 2

C. 4

D. √2

Answers

Answer:

u=2 root 2

Step-by-step explanation:

All 45 45 90 degree triangles follow the same pattern

Hi, can you help me with these?
It's really hard :(​

Answers

Rachel will earn $85 in 10 hours :)

Here's the Solution:

Direct Variation

Y = kx

Given:

$34=k(4)

k = 34/4

k = 17/2

Y = kx

Y = (17/2) (10)

Y = 85

Hope this helps :)

The vertical side of a right triangle measures 6 inches, and the horizontal side measures 8 inches
1.Write the ratio of the distance of the vertical side to the distance of the horizontal side as a reduced fraction
2.If the original triangle were enlarged by 3 times, what would the new dimensions be?
3.Does the ratio of vertical side to horizontal side change when scaling up? Explain.

Answers

9514 1404 393

Answer:

3/4vertical: 18 in; horizontal: 24 inno change

Step-by-step explanation:

1. The ratio is ...

  (6 in)/(8 in) = 6/8 = 3/4

__

2. The scaled dimensions are ...

  6 in × 3 = 18 in (vertical side)

  8 in × 3 = 24 in (horizontal side)

__

3. You know from your process of reducing the fraction in part 1 that multiplying numerator and denominator by the same value does not change the reduced ratio.

I will mark as brainliest if you can answer. :)

Answers

not enough information

Someone please help me on this!
Which statements are true about the
transformation (x,y) → (x - 1 y +4)?
A The transformation is a non-rigid
motion.
B The transformation slides the figure
to the left 1 unit and up 4 units.
C The transformation is a rigid motion.
D The transformation slides the figure to
the right 1 unit and down 4 units.

Answers

Answer:

b and c

Step-by-step explanation:

b is obvious since you can just plug In a point to solve

but c is a bit trickier a rigid motion is a transformation that doesn't change size or shape and we are just moving points which have same size so c is true.

Y varies directly with x and y=8 when x=-5

Answers

Answer:

Y=K×X...... equation

When,Y=8 and X=-5

To find the constant (K)

we substitute for K in the equation

8=K×-5

8=-5K divide both sides by -5

8÷-5=-5K÷-5

K=-1.6

A total of 621 tickets were sold for the school play day for the school play they were either adult tickets or student tickets it there were 71 more student to get sold then adult tickets how many adult tickets were sold

Answers

Answer:

275 student tickets and 346 adult tickets

Step-by-step explanation:

621-71=550

550÷2=275+71346