Question

The perimeter of Square A is 24 linear units. The area of Square B is 4 times the area of Square A. What is the area of Square B? What is the perimeter of Square B?show your work

Answer 1

area of Square B: 144 quadratic units

perimeter of Square B: 48 linear units

Explanation:

The perimeter of a square is

perimeter = 4*L

where L is the length of each square side. For square A:

24 = 4*L

L = 24/4

L = 6 linear units

The area of a square is

area = L^2

For square A:

area = 6^2 = 36 quadratic units

The area of Square B is 4 times the area of Square A. So

area of Square B = 4*area of Square A

area of Square B = 4*36

area of Square B = 144 quadratic units

And the length of the sides of the square B can be computed as

area = L^2

L = sqrt(area)

L = sqrt(144)

L = 12 linear units

Therefore, the perimeter of square B is

perimeter = 4*L

perimeter = 4*12

perimeter = 48 linear units

Answer 2

Area of Square B is 144, divided 24 by 4 to get 6 for one side, multiplied by 6 to get the total area of Square A and then multiplied by 4 to get the area of Square B.

The perimeter of Square B is 48 because 12 x 12 = 144, so 12 + 12 + 12 + 12 = 48