Chapter 11.7, Problem 13PSB

To determine

To calculate:Thearea of larger triangleABC.

Answer to Problem 13PSB

The area of larger triangle ABCis $250$ .

Explanation of Solution

Given information:

  $\frac{AB}{PQ}=\frac{5}{2}$

  $A(PQR)=40$

Formula used:

The below property is used:

Area of triangle is proportional to square of its side.

Calculation:

  

Area of triangle is proportional to square of its side.

  $\begin{array}{l}\frac{A(ABC)}{A(PQR)}=\frac{{(AB)}^2}{{(PQ)}^2}\\ \frac{A(ABC)}{40}={\left(\frac{AB}{PQ}\right)}^2\\ \frac{A(ABC)}{40}={\left(\frac{5}{2}\right)}^2\\ \frac{A(ABC)}{40}=\left(\frac{25}{4}\right)\\ A(ABC)=\frac{25\times 40}{4}\\ A(ABC)=250\end{array}$