Question

Explain why the two triangles below are similar by writing the appropriate similarity theorem. Then find x. Round your answer to the nearest tenth. (example answer ---> SSS,9.2 ---> no spaces)

Answer 1

Answer:

SSS Theorem

$x = 35.7$

Step-by-step explanation:

Given

The attached triangle

Solving (a) The similarity theorem

The given sides of the triangle are similar.

In other words, they are similar by sides.

Hence, the theorem is: SSS

Solving (b): Find x

To find x, we make use of the following equivalent ratios.

$\frac{14}{25} = \frac{14+6}{x}$

This gives:

$\frac{14}{25} = \frac{20}{x}$

Cross multiply

$14 * x = 20 * 25$

$14 * x = 500$

Solve for x

$x = \frac{500}{14}$

$x = 35.7$ -- approximated