Question

A rectangle has an area of 105 square feet. If the sum of the length and the width is 26 feet, find the dimensions. Include units in your answer.

Answer 1

L x W = 105

L + W = 26 so L = 26 - W

substitute L = 26 - W into L x W = 105

(26 - W) x W = 105

26W - W^2 = 105

W^2 - 26W + 105 = 0

(W - 21)(W - 5) = 0

W - 21 = 0; W = 21

W - 5 = 0; W = 5

The the dimensions of the rectangle are 5 ft and 21 ft.

Double check:

The sum of the length and the width is 26 feet: 21 + 5 = 26 feet

A rectangle has an area of 105 square feet: 21 x 5 = 105 square feet

Answer 2

Let one dimension be x and the other dimension be y.

The area is 105 ft²

⇒ xy = 105

The length and width adds up to 26 ft

⇒ x + y = 26

System of equations:

xy = 105 --------- (1)

x + y = 26 ----------(2)

From (2):

x + y = 26

x = 26 - y --------- sub into (1)

(26 - y)y = 105

26y - y² = 105

y² - 26y + 105 = 0

(y - 5)(y - 21) = 0

y = 5 or y = 21

Answer: The dimensions of the rectangle is 5 feet by 21 feet