Question

Use the diagram below to solve for x and y.

Answer 1

Option A. x=30,y=42

Explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and ZYX have three congruent interior angles

therefore

Triangles are similar

step 1

Find the value of x

`(ZY)/(AB)=(ZX)/(AC)`

substitute the values

`(20)/(x)=(12)/(18)`

`x=20*18/12=30\ units`

step 2

Find the value of y

`(ZY)/(AB)=(XY)/(CB)`

substitute the values

`(20)/(30)=(28)/(y)`

`y=30*28/20=42\ units`