SOLUTION: The area of a rectangular conference room is represented by the equation A = (x2 + 17x + 72) feet2. If x = 6 feet and the width = (x + 8) feet, what is the perimeter, in feet,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The area of a rectangular conference room is represented by the equation A = (x2 + 17x + 72) feet2. If x = 6 feet and the width = (x + 8) feet, what is the perimeter, in feet,       Log On


   

Question 811419: The area of a rectangular conference room is represented by the equation A = (x2 + 17x + 72) feet2.
If x = 6 feet and the width = (x + 8) feet, what is the perimeter, in feet, of the room?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for the area of a rectancle is A = L * W.
The equation for the perimeter of a rectangle is P = 2L + 2W.
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Given: X = 6
Given: A+=+X%5E2+%2B+17X+%2B+72
Given: W+=+X+%2B+8
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Since we know that X = 6, we can solve for W.
W+=+X+%2B+8
W+=+%286%29+%2B+8
highlight%28W+=+14%29
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Now we can solve for the area by plugging 6 into the equation for X.
Given: A+=+X%5E2+%2B+17X+%2B+72
A+=+%286%29%5E2+%2B+17%2A%286%29+%2B+72
Simplify
A+=+36+%2B+102+%2B+72
Combine like terms.
highlight_green%28A+=+210%29
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Now we can solve for the length.
A+=+L%2AW
210+=+L+%2A+%2814%29
Divide both sides by 14.
highlight%2815+=+L%29
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Now we can use the perimeter equation.
P+=+2L+%2B+2W
P+=+2%2A%2815%29+%2B+2%2A%2814%29
Simplify
P+=+30+%2B+28
highlight_green%28P+=+58%29
The perimeter of the room is 58 feet.