Chapter 11, Problem 20CUR

To determine

To Find: Ratio of perimeters and ratio of areas of the rectangles.

Answer to Problem 20CUR

Ratio of area = $4:3$

Ratio of perimeter = $2:\sqrt{3}$

Explanation of Solution

Given:

Two similar rectangles with diagonals $6\sqrt{3}$ and 9.

Ratio of area of two similar rectangles is equal to the square of ratio of the diagonals.

Therefore, the ratio of area of given rectangles is:

  ${(6\sqrt{3})}^2:9^2\Rightarrow 108:81\Rightarrow 4:3$

Ratio of perimeter of two similar rectangles is equal to the ratio of the diagonals.

Therefore, the ratio of perimeter of given rectangles is:

  $6\sqrt{3}:9\Rightarrow 2\sqrt{3}:3\Rightarrow 2:\sqrt{3}$