Question

δabc ~ δdef
find the value of x.
a 15 m c
6 m
b
d 5 m f
x m
e
x = ?

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. So, $\frac{AB}{DE}=\frac{AC}{DF}$. Substituting the given values, we get $\frac{6}{x}=\frac{15}{5}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{6}{x}=\frac{15}{5}$ gives us $15x = 6\times5$.

Step3: Solve for x

First, calculate $6\times5 = 30$. Then we have $15x=30$. Divide both sides by 15: $x=\frac{30}{15}=2$.

Answer:

$2$