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Write an equation for each statement:
"the perimeter of a rectangle is 100ft"
2L + 2W = 100
Simplify, divide thru by 2, results
L + W = 50
To use for substitution later, write it:
L = (50-W)
"the area is 400ft(squared)"
L * W = 400
From the perimeter; replace L with (50-W) in the above equation
(50-W) * W = 400
50W - W^2 = 400
Arrange as a quadratic equation
-W^2 + 50W - 400 = 0
Easier to factor if we change the signs, multiply by -1, results:
W^2 - 50W + 400 = 0
(W-40)(W-10) = 0
W = 40
W = 10
.find the dimensions of the rectangle.
If W = 40, remember L = (50-W), then
L = 50 - 40
L = 10
If W = 10, then
L = 50 - 10
L = 40
Generally the length is the longer dimension so 40 by 10 would be the answer
You can check this solution by finding the perimeter with these values
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