Question

△jkl ~ △fgh. find the values of x and y.

Explanation:

Step1: Set up ratio for corresponding sides

Since $\triangle{JKL}\sim\triangle{FGH}$, the ratios of corresponding sides are equal. For the sides $LJ$ and $HF$, we have $\frac{LJ}{HF}=\frac{20}{15}=\frac{4}{3}$.

Step2: Find the value of $x$

For side $LK$ and $HG$, $\frac{LK}{HG}=\frac{4}{3}$. Substituting the values, $\frac{12}{x}=\frac{4}{3}$. Cross - multiply gives $4x = 12\times3$, so $4x=36$ and $x = 9$.

Step3: Find the value of $y$

For side $KJ$ and $GF$, $\frac{KJ}{GF}=\frac{4}{3}$. Substituting the values, $\frac{16}{y}=\frac{4}{3}$. Cross - multiply gives $4y=16\times3$, so $4y = 48$ and $y = 12$.

Answer:

$x = 9$, $y = 12$