What are the side lengths of the rectangle area 40 perimeter 26

Recall the formula for finding the area of a rectangle:

Area = Length * Width

Recall the formula for finding the perimeter of a rectangle:

Perimeter = 2 (Length + Width)

Given in your problem:

Area = 40 sq. units

Perimeter = 26 units

Required to solve for:

Length (L) and width (W)

• First, substitute the given to the formula:

Area = Length x Width

40 = L * W ⇒ equation number 1

Perimeter = 2 (Length + Width)

26 = 2 (L + W) ⇒ equation number 2

• Simplifying equation number 2,

13 = L + W

• Rearranging the equation,

L = 13 - W ⇒ equation 3

Substituting equation 3 from equation 1:

(equation 1) 40 = (L) (W)

(equation 3) L = 13 - W

40 = (13 - W) (W)

40 = 13W - W²

(regrouping) W² - 13W + 40 = 0

(factoring) (W - 8) (W - 5) = 0

W - 8 = 0; W - 5 = 0

W = 8; W = 5

Therefore, there are 2 possible values for the width of the rectangle. It can be 8 units or 5 units.

• Now to solve for the length of the rectangle, substitute the two values of width to equation 3.

(equation 3) L = 13 - W

for W = 8 ⇒ L = 13 - 8

L = 5 units

for W = 5 ⇒ L = 13 - 5

L = 8 units