Question

find the length of side x and side y given that the triangles are similar.

x = , y = (simplify your answers.)

Explanation:

Step1: Find the scale - factor

The ratio of corresponding sides of similar triangles is the same. Let's find the scale - factor by comparing the known corresponding sides. The ratio of the side of length 55 in the first triangle to the side of length 10 in the second triangle is $\frac{55}{10}=\frac{11}{2}$.

Step2: Find side x

Side x corresponds to side 110. Using the scale - factor, we have $x=\frac{110}{\frac{11}{2}}=110\times\frac{2}{11} = 20$.

Step3: Find side y

Side y corresponds to side 99. Using the scale - factor, we have $y=\frac{99}{\frac{11}{2}}=99\times\frac{2}{11}=18$.

Answer:

$x = 20$, $y = 18$