Question

ABC ~ AXYZ. Using the information in the diagram, find the area of AXYZ.

Answer 1

It is given that the triangles are similar, that is,

`\triangle ABC\sim\triangle XYZ`

It is required to find the area of the larger triangle.

Recall that the scale factor, k of similar figures is the ratio of their corresponding sides:

`k=(AC)/(XZ)`

Substitute AC=5 and XZ=15 into the equation:

`k=(5)/(15)=(1)/(3)`

Hence, the scale factor is 1/3.

Recall that as per the Area of Similar Figures, the ratio of areas for two similar figures with a scale factor, k is:

`k^2`

This implies that:

`\frac{\text{area of }\triangle ABC}{\text{area of }\triangle XYZ}=k^2`

Substitute the values of the area of triangle ABC and the scale factor into the proportion:

`\Rightarrow\frac{48}{\text{area of }\triangle XYZ}=((1)/(3))^2`

Let the area of ΔXYZ be A, and solve for A in the equation:

`\begin{gathered} (48)/(A)=(1)/(9) \\ \Rightarrow A=9*48=432ft^2 \end{gathered}`

The required answer is 432 square ft.

The last choice is the answer.