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

SSS Theorem

`x = 35.7`

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.

`(14)/(25) = (14+6)/(x)`

This gives:

`(14)/(25) = (20)/(x)`

Cross multiply

`14 * x = 20 * 25`

`14 * x = 500`

Solve for x

`x = (500)/(14)`

`x = 35.7` -- approximated