Chapter 11.5, Problem 30STP

To determine

To Find: The correct option for the area of the triangle $\Delta ABC$ .

Answer to Problem 30STP

The correct option is D

Explanation of Solution

Given:

The $\Delta ABC$ is equivalent to the triangle $\Delta PRT$ .

The value of $AC=15\text{inches}$ and value of $\Delta ABC$ is $24{\text{in}}^2$ .

Calculation:

Consider the scale factor for the two triangle is,

  $\begin{array}{c}k=\frac{AC}{PT}\\ =\frac{15}{6}\\ =\frac{5}{2}\end{array}$

Then, by the theorem of similar polygon.

  $\begin{array}{l}{\left(\frac{5}{2}\right)}^2=\frac{A}{24}\\ A=\left(\frac{25}{4}\right)\left(24\right)\\ A=150\end{array}$

Thus, the correct option is D