Chapter 11.7, Problem 5PSA

To determine

To Calculate: The ratio of a pair of corresponding altitudes.

Answer to Problem 5PSA

The ratio of a pair of corresponding altitudes is $3:4$

Explanation of Solution

Given information: Ratio of the areas of two similar polygons is $9:16$

  

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, $\frac{A{D}^2}{P{S}^2}=\frac{ar(\Delta ABC)}{ar(\Delta PQR)}$

  $\frac{A{D}^2}{P{S}^2}$ = $\frac{9}{16}$

  $\frac{AD}{PS}=\frac{3}{4}$

Conclusion: Hence,the ratio of a pair of corresponding altitudes is $3:4$