Question

The length of a rectangle is twice the width. Given that the perimeter of the rectangle is 24 feet, how many square feet are in the area of the rectangle?

Answer 1

Area = 32feet²

Explanation:

Perimeter of a rectangule = 2(length+width)

Then:

g = 2w Eq. 1

2(g+w) = 24 Eq. 2

g = length

w = width

From Eq. 2:

(2*g + 2*w) = 24

2g + 2w = 24

2w = 24 - 2g Eq. 3

Matching Eq. 1 and Eq. 3

g = 24 - 2g

g + 2g = 24

3g = 24

g = 24/3

g = 8 feet

From Eq. 1

g = 2w

8 = 2w

8/2 = w

w = 4 feet

Check:

From Eq. 2

2(g+w) = 24

2(8+4) = 24

2*12 = 24

Answer:

Area of a rexctangle = length * width

Then:

Area = 8feet * 4feet

Area = 32feet²