SOLUTION: Using a quadratic equation (if possible) please solve the following: The perimeter of a rectangle is 54 meters and its area is 180 sq. meters. Find its length and width.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Using a quadratic equation (if possible) please solve the following: The perimeter of a rectangle is 54 meters and its area is 180 sq. meters. Find its length and width.       Log On


   

Question 841878: Using a quadratic equation (if possible) please solve the following:
The perimeter of a rectangle is 54 meters and its area is 180 sq. meters. Find its length and width.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y the two dimensions.
2x%2B2y=54, perimeter equation.
highlight_green%28x%2By=27%29, perimeter equation simplified.
Area, highlight_green%28xy=180%29.
Use simple substitution and solve the quadratic equation which results.


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y=27-x;
xy=x%2827-x%29=180
-x%5E2%2B27x-180=0
x%5E2-27x%2B180=0
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x=%2827%2Bsqrt%2827%5E2-4%28180%29%29%29%2F2
x=%2827%2Bsqrt%289%29%29%2F2
highlight%28x=15%29
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