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
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
