Question

The length of a rectangular box is 2 units less than its width.

If the area of the box is 15 units square.
Find the perimeter of the box.

Answer 1

L = W - 2

A = L x W
A = (W - 2) x W
A = W^2 - 2W
15 = W^2 - 2W
W^2 - 2W - 15 = 0
(W -5)(W + 3 ) = 0
W - 5 = 0; W = 5
W - 3 = 0; W = -3

so Width = 5
Length = 5 - 2 = 3

P = 2(5 +3)
P = 2 (8)
P = 16
answer: P = 16 units

Answer 2

L=W-2

A=LW and using L from above and A=15

(W-2)W=15

W^2-2W-15=0

W^2-5W+3W-15=0

W(W-5)+3(W-5)=0

(W+3)(W-5)=0, and W>0 so

W=5, and since L=W-2

L=3

The perimeter P is

P=2L+2W=2(L+W)

P=2(3+5)

P=16 units