Question

△jkl ~ △fgh. find the values of x and y.
l 20 j
12
16
k
h 15 f
x y
g
13

Explanation:

Step1: Find the scale - factor

Since $\triangle{JKL}\sim\triangle{FGH}$, the ratio of corresponding sides is equal. The ratio of the side lengths of $\triangle{JKL}$ to $\triangle{FGH}$ for the pair of known corresponding sides $\frac{JL}{FH}=\frac{20}{15}=\frac{4}{3}$.

Step2: Find the value of $x$

Side $KL$ corresponds to side $HG$. We know that $\frac{KL}{HG}=\frac{4}{3}$. Given $KL = 12$, then $\frac{12}{x}=\frac{4}{3}$. Cross - multiply: $4x=12\times3$, so $4x = 36$, and $x = 9$.

Step3: Find the value of $y$

Side $JK$ corresponds to side $FG$. We know that $\frac{JK}{FG}=\frac{4}{3}$. Given $JK = 16$, then $\frac{16}{y}=\frac{4}{3}$. Cross - multiply: $4y=16\times3$, so $4y = 48$, and $y = 12$.

Answer:

$x = 9$, $y = 12$