Question

The perimeter of a rectangle is 44ft , and the area of the rectangle is 40ft^2 . Find the dimensions of the rectangle.

Answer 1

Are you sure about the measurements?

Answer 2

yes

Answer 3

The equation of the perimeter of a rectangle is P = 2L + 2W and the equation for the area of the rectangle is A = LW

Equation 1
A = LW
40 = LW
L = 40/W this is our 1st equation

We will then substitute equation 1 to the equation of the Perimeter
P = 2L+2W
44 = 2(40/W) + 2W
Multiply both sides by W
W(44 = 2(40/W) + 2W)W
44W = 80 + 2W^2
0 = 2W^2 -44W +80

Use Quadratic Formula
0 = (W - 20) (W - 2)

We then have 2 values of W
W = 20 or W = 2

Substitute a value of W to the equation of a Area
A = LW
40/W = L
40/20 = L
2 = L

Substitute the other value of W
A = LW
40/W = L
40/2 = L
20 = L

We therefore conclude that if the W = 20 then the corresponding Length is 2
and when the W = 2 then the corresponding Length is 20