Question

How do i do this question?

Answer 1

The length of BC = 72

Solution:

Given ΔABC and ΔDEF are similar triangles.

ΔABC $\sim$ ΔDEF

AB = 54, BC = n, EF = 12, DE = 9

Similar triangle theorem:

If two triangles are similar then the corresponding sides are proportional to each other.

$\Rightarrow\frac{BC}{EF}=\frac{AB}{DE}$

Substitute the given values, we get

$\Rightarrow\frac{n}{12}=\frac{54}{9}$

Do cross multiplication.

$\Rightarrow9\times n=54\times12$

Divide both sides of the equation by 9.

$\Rightarrow n=\frac{54\times12}{9}$

$\Rightarrow n=6\times12$

$\Rightarrow n=72$

⇒ BC = 72

Option B is the correct answer.

The length of BC = 72.