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Lorico [155]
3 years ago
14

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 unit

s in your answer.
Mathematics
2 answers:
Andrei [34K]3 years ago
8 0

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



Oksanka [162]3 years ago
7 0

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

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