Find the area by solving algebraically

Question

The length of the rectangle is 14 less than three times it’s width. If it’s perimeter is 92 feet, find it’s area.

Answer 1

Let L be the length of the rectangle and W be the width of the rectangle.

The length of the rectangle is 14 less than three times it’s width means: L=3W-14.

Using the perimeter formula of the rectangle P=2(L+W) we have

92=2(3W-14+W)

Solve for W:

92=6W-28+2W

92=8W-28

92+28=8W

120=8W

W=15

We can find the length L=3W-14= 3• 15-14=45-14=31

Area of the rectangle is A=L•W=31•15=465

Answer 2

2(3w-14) + 2w = 92

6w - 28 + 2w = 92

8w - 28 = 92

8w = 120

w=15

The rectangle has dimensions length = 31 and width 15