Question

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

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. So, $\frac{BC}{EF}=\frac{AC}{DF}$, which gives $\frac{9}{x}=\frac{15}{5}$.

Step2: Cross - multiply

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

Step3: Simplify right - hand side

$9\times5=45$, so $15x = 45$.

Step4: Solve for x

Dividing both sides of $15x = 45$ by 15, we get $x=\frac{45}{15}=3$.

Answer:

$3$