Chapter 3, Problem 6E

To determine

To find : the area of the smaller triangle.

Answer to Problem 6E

216 square centimeters

Explanation of Solution

Given information: The sides of two similar triangles are in the ratio of 3:5. The area of the larger triangle is 600 square centimeters.

Calculation:

Let $A_1$ and $A_2$ be the area of the smaller triangle and bigger triangle respectively.

We know that if the two triangles are similar , then ratio of the area of both the triangles is proportional to the square of the ratio of their corresponding sides.

Therefore,

  $\begin{array}{l}\frac{A_1}{A_2}={\left(\frac{3}{5}\right)}^2\\ \frac{A_1}{A_2}=\frac{9}{25}\end{array}$

Now, area of bigger triangle is 600 square centimeters, that is $A_2=600c{m}^2$

Therefore, we have

  $\begin{array}{l}\frac{A_1}{600}=\frac{9}{25}\\ A_1=\frac{9}{25}\times 600\\ A_1=216c{m}^2\end{array}$

Thus, area of smaller triangle is 216 square centimeters.