SOLUTION: The area of a rectangle is 39 square feet and twice the length is 5 feet shorter than 3 times the width. What is the perimeter?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The area of a rectangle is 39 square feet and twice the length is 5 feet shorter than 3 times the width. What is the perimeter?      Log On


   

Question 798724: The area of a rectangle is 39 square feet and twice the length is 5 feet shorter than 3 times the width. What is the perimeter?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = width
Let y = length
Given used, xy=39;
2y=-5%2B3x.
Rectangle Fact justifies 2x%2B2y=perimeter

You first want to solve for x and y. You can find perimeter when you know x and y.


SOLUTION:
More than one way to do this. You'll solve for one variable from one of the "given" described equations, substitute this into the other equation, and solve for the single variable; then use the value to solve for the other variable.

A SOLUTION CHOICE:
xy=39
y=39%2Fx.
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2%2A%2839%2Fx%29=-5%2B3x, substituting into the other equation...
78=-5x%2B3x%5E2
3x%5E2-5x-78=0, QUADRATIC EQUATION
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Discriminant, 5%5E2-4%2A3%28-78%29=25%2B12%2A78=961, to be neat, this would be a square value.
... LUCK! sqrt%28961%29=31.
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Directly using general solution to a quadratic equation:
highlight%28x=%285%2B-+sqrt%28discriminant%29%29%2F%282%2A3%29%29
We KNOW we want the positive value, and NOT the negative value.
highlight%28x=%285%2B31%29%2F%282%2A3%29%29
highlight%28x=6%29 and so y=39%2F6=highlight%286%261%2F2%29

Perimeter is simply 2%286%2B6%261%2F2%29=13 feet.