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;
[tex]\frac{AC}{FH}=\frac{AB}{GF}=\frac{BC}{GH}[/tex]
Let us consider the proportion [tex]\frac{AB}{GF}=\frac{BC}{GH}[/tex] to determine the value of x.
Substituting AB = 9 cm, GF = 13.5 cm, BC = 15 cm and GH = x, we get;
[tex]\frac{9}{13.5}=\frac{15}{x}[/tex]
Cross multiplying, we get;
[tex]9x=15 \times 13.5[/tex]
[tex]9x=202.5[/tex]
[tex]x=22.5 \ cm[/tex]
Thus, the value of x is 22.5 cm
Hence, Option F is the correct answer.
