The combined area of two squares is 153 square meters. The sides of the larger square are 4 times as long as the sides of the smaller square. Find the dimensions of each of the squares.
A)Dimensions of the smaller square are 4 by 4 meters, dimensions of the larger square are 16 by 16 meters.
B)Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 4 by 4 meters.
C)Dimensions of the smaller square are 8 by 8 meters, dimensions of the larger square are 32 by 32 meters.
D)Dimensions of the smaller square are 3 by 3 meters, dimensions of the larger square are 12 by 12 meters.
E)Dimensions of the smaller square are 2 by 2 meters, dimensions of the larger square are 8 by 8 meters.

Question

Quizplus · Accepted Answer

Let the side of the smaller square be x meters. Then the side of the larger square is 4x meters. The area of the smaller square is x^2 and the area of the larger square is (4x)^2 = 16x^2. The combined area is x^2 + 16x^2 = 17x^2 = 153. Solving for x gives x^2 = 9, so x = 3. Thus, the smaller square is 3 by 3 meters and the larger square is 12 by 12 meters.

The Combined Area of Two Squares Is 153 Square Meters