SOLUTION: a rectangular garage that has an area of 198 ft, the length is 7 ft longer than the width, what is the length of the garage.?

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Question 862707: a rectangular garage that has an area of 198 ft, the length is 7 ft longer than the width, what is the length of the garage.?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle has an area A, and the length L is k longer than the width w. What is L, or find a formula for L.

Unknown variables are w and L.

wL=A and L=w%2Bk; using this formula for L, w=L-k.
Returning to the area relationship,
w%2AL=A
%28L-k%29L=A
highlight_green%28L%5E2-kL-A=0%29
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The numbers A%3E0 and k%3E0, so the usage of signs for the solution for L are unmistakable. Use the solution for the general solution to a quadratic equation with the positive square root form.
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L=%28k%2Bsqrt%28k%5E2-4%2A%28-A%29%29%29%2F2
highlight%28L=%28k%2Bsqrt%28k%5E2%2B4A%29%29%2F2%29

You can make the substitutions of k=7 and A=198 and compute L.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

a rectangular garage that has an area of 198 ft, the length is 7 ft longer than the width, what is the length of the garage.?


Let width's measurement be W

Then length = W + 7

Therefore, W(W + 7) = 198

W%5E2+%2B+7W+-+198+=+0

Solve for W, or width, discarding the negative (< 0) value

Add 7 to the value of W, or width to determine value of length

You can do the check!! 



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