Chapter 11.7, Problem 4PSA

To determine

To Calculate: The ratio of triangle’s area.

Answer to Problem 4PSA

The ratio of triangle’s area is $16:81$

Explanation of Solution

Given information: Pair of corresponding sides of two similar triangles are $4$ and $9$

  

Concept used: The property of similar triangles: ratio of areas of two similar triangles is equal to ratio of squares of their corresponding side.

Calculation: Here, $\frac{A{B}^2}{P{Q}^2}=\frac{ar(\Delta ABC)}{ar(\Delta PQR)}$

  ${\left(\frac{4}{9}\right)}^2$ = $\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}$

  $\frac{16}{81}=\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}$

So, the ratio is

  → $16:81$

Conclusion: Hence,the ratio of triangle’s area is $16:81$