Question

△abc ~ △def
find the value of x.
a
12 m
b
21 m
c
d
4 m
e
x m
f
x = ?

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding - sides are equal. So, $\frac{AB}{DE}=\frac{BC}{EF}$. Here, $AB = 12$ m, $DE = 4$ m, $BC = 21$ m, and $EF=x$ m. The proportion is $\frac{12}{4}=\frac{21}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{12}{4}=\frac{21}{x}$ gives us $12x=4\times21$.

Step3: Solve for x

First, calculate $4\times21 = 84$. Then, we have the equation $12x = 84$. Divide both sides of the equation by 12: $x=\frac{84}{12}=7$.

Answer:

$7$