Question 156292: The width of a rectangle is 5ft. less then the length. The area of the rectangle is 176ft^2 Find the length and width of the rectabgle. I tried looking in my math and other books for examples and can't seem to find one.Please help
Thanks
Answer by kdr(11)   (Show Source):
You can put this solution on YOUR website! Let L be the length of the rectangle. Let W be the width.
The area of a rectangle is found by multiplying the length times the width.
So, Area = LW
But we know the area is 176 ft.^2, so we can write this equation:
176 ft^2 = LW
We also know the width is 5 ft. less than the length, so we can write this equation:
W = L - 5
Now, substitute L-5 for W in the first equation:
176 = L(L-5)
176 = L^2 - 5L
0 = L^2 - 5L -176
Factoring gives us:
0 = (L + 11)(L - 16)
So, either
L + 11 = 0
giving
L = -11
or
L - 16 = 0
giving
L = 16
Since the length of the rectangle cannot be a negative value, the length, L, is 16.
Since W = L - 5,
W = 16 - 5
W = 11
The length of the rectangle is 16 feet, the width is 11 feet.
Checking:
Area = L*W
176 ft^2 = (16 ft)(11 ft)
176 ft^2 = 176 ft^2
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