Question

A rectangle has length 12 feet and width 8 feet. Every dimension of the rectangle is multiplied by 3/4 to form a similar rectangle. How is the ratio of the areas related to the ratio of corresponding side

Answer 1

Let the area of the original rectangle be A₁.

A₁ = (12 ft)(8 feet) = 96 ft²

To determine the area of the reduced triangle, let's compute the new dimensions first.

Length = 12 ft * 3/4 - 9 ft
Width = 8 ft *3/4 = 6 ft

Thus, the area of the new rectangle denoted as A₂ is
A₂ = (9 ft)(6 ft) = 54 ft

The ratio of the areas are:
A₂/A₁ = 54/96 = 9/16
The ratio of the sides are given to be 3/4.
Finally the ratios of the area to side would be:
Ratio = 9/16 ÷ 3/4 = 3/4

Therefore, the ratio of the areas is 3/4 of the ratio of the corresponding sides.