Question

Logan is flying a kite that is made up of three similar rectangles. The sides of the three rectangles are in the ratio 1:2:3. If the area of the smallest rectangle is 72 square inches, what are the areas of the other two rectangles?

Answer 1

`288,648`

Explanation:

Area of rectangle `A_R=a*b`, where `a`=length, `b`=width.

Given that the sides of the three similar rectangles are in the ratio of `1:2:3`,

Let the sides of the three similar rectangles be `a, b, 2a, 2b, 3a, 3b`, respectively.

Given that area of the smallest rectangle `= a*b=72`

`=> 2a*2b=4ab=4*72=288`

`=> 3a*3b=9ab=9*72=648`

Hence, the area of the other two rectangles are `288`, and `648`, respectively.

SIde note : if the sides of three similar rectangles are in the ratio of `1:2:3`. their areas will be in the ratio of `1:2^2:3^2=1:4:9`.