What is the value of x? Enter your answer in the box.

x = 9

Step-by-step explanation:

Similar Triangles

We are given a shape where two similar triangles are given. The similarity theorem states that the side lengths of the triangles must be proportional in the same scale factor.

The total length of the left side is 72+9 = 81 cm

The smaller length of the left side is 9 cm

The proportion is 81/9 = 9. This is the scale factor.

The total length of the right side is 3x - 20 + 56 = 3x + 36

The smaller length of the right side is 3x-20

The proportion must be equal to 9:

Multiplying by 3x-20:

3x+36=9(3x-20)

Operating

3x+36=27x-180

Rearranging:

24x = 216

Dividing by 24:

x = 9

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.