Question

△abc ~ △def
find the value of x.
a
d
15 ft
5 ft
e
x ft
f
b
9 ft
c
x = ?

Explanation:

Step1: Set up proportion for similar triangles

For similar triangles $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. So, $\frac{BC}{EF}=\frac{AC}{DF}$. Substituting the given values, we get $\frac{9}{x}=\frac{15}{5}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{9}{x}=\frac{15}{5}$ gives us $15x = 9\times5$.

Step3: Simplify and solve for x

First, calculate $9\times5 = 45$. So, $15x=45$. Then, divide both sides by 15: $x=\frac{45}{15}=3$.

Answer:

$3$