Question

Triangle ABC is similar to Triangle FGH. What is the value of x in centimeters?

Answer 1

Given:

Given that the triangle ABC is similar to triangle FGH.

We need to determine the value of x.

Value of x:

Since, the triangles are similar, then their sides are proportional.

Thus, we have;

$\frac{AC}{FH}=\frac{AB}{GF}=\frac{BC}{GH}$

Let us consider the proportion $\frac{AB}{GF}=\frac{BC}{GH}$ to determine the value of x.

Substituting AB = 9 cm, GF = 13.5 cm, BC = 15 cm and GH = x, we get;

$\frac{9}{13.5}=\frac{15}{x}$

Cross multiplying, we get;

$9x=15 \times 13.5$

$9x=202.5$

 $x=22.5 \ cm$

Thus, the value of x is 22.5 cm

Hence, Option F is the correct answer.