Question

δabc ~ δdef
find the value of x.
a
8 ft
d
x ft
e 3 ft f
b 6 ft c
x = ?

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal. So, $\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}$. We can use the ratio of the sides $\frac{AC}{DF}=\frac{BC}{EF}$. Substituting the given values, we get $\frac{8}{x}=\frac{6}{3}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{8}{x}=\frac{6}{3}$ gives us $6x = 8\times3$.

Step3: Solve for x

First, calculate $8\times3 = 24$. So, $6x=24$. Then divide both sides by 6: $x=\frac{24}{6}=4$.

Answer:

$x = 4$