SOLUTION: what is the length and width if the area of a rectangle is 54 ft squared and the perimeter is 42ft

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Question 773179: what is the length and width if the area of a rectangle is 54 ft squared and the perimeter is 42ft
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Length * Width = Area = 54ft
L * W = 54 => W = 54/L
Perimeter = 2* Length + 2* Width
Perimeter = 2L + 2W
Replace W with 54/L
Perimeter = 2L + 2(54/L)
42ft = 2L + 108/L
Common denominator = L
42L = 2L^2 + 108
Rearrange.
2L^2 - 42L + 108 = 0
Divide by 2
L^2 - 21L + 54 = 0
(L - 3)(L - 18) = 0
L - 3 = 0
L = 3
L - 18 = 0
L = 18
therefore either the length
= 18ft and the width = 3ft.
OR
the length = 3ft and the width
= 18ft.
Hope this helps.
:-)