SOLUTION: The rectangle has a perimeter of 5 units. What is the value of x? The length is 3/(x+2) and the width is 2/(x-3).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The rectangle has a perimeter of 5 units. What is the value of x? The length is 3/(x+2) and the width is 2/(x-3).      Log On


   

Question 917641: The rectangle has a perimeter of 5 units. What is the value of x?
The length is 3/(x+2) and the width is 2/(x-3).
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The rectangle has a perimeter of 5 units. What is the value of x?
The length is 3/(x+2) and the width is 2/(x-3).
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Perimeter = 2(length + width)
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5 = 2[(3/(x+2))+(2/(x-3)]
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5(x+2)(x-3) = 2[3(x-3) +2(x+2)]
5[x^2-x-6] = 2[3x-9+2x+4]
5x^2 - 5x - 30 = 10x -10
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5x^2 -15x -20 = 0
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x^2 -3x - 4 = 0
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Factor:
(x-4)(x+1) = 0
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x = 4 or x = -1
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Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The rectangle has a perimeter of P=5 units.
The length is L=3%2F%28x%2B2%29+ and the width is W=+2%2F%28x-3%29+.
P=2%28L%2BW%29
What is the value of x?
5=2%283%2F%28x%2B2%29+%2B2%2F%28x-3%29%29
5=%286%28x-3%29%2F%28%28x%2B2%29%28x-3%29%29%2B4%28x%2B2%29%2F%28%28x-3%29%28x%2B2%29%29+%29
5=%286x-18%2B4x%2B8%29%29%2F%28%28x-3%29%28x%2B2%29%29+
5=%2810x-10%29%29%2F%28%28x-3%29%28x%2B2%29%29+
5%28x-3%29%28x%2B2%29=10x-10+
5%28x%5E2%2B2x-3x-6%29=10x-10+
5x%5E2%2B10x-15x-30-10x%2B10=0+
5x%5E2-15x-20=0+
5x%5E2%2F5-15x%2F5-20%2F5=0+
x%5E2-3x-4=0+
x%5E2%2Bx-4x-4=0+
%28x%5E2%2Bx%29-%284x%2B4%29=0+
x%28x%2B1%29-4%28x%2B1%29=0+
%28x-4%29%28x%2B1%29=0+
solutions:
x-4=0+ => x=4
x%2B1=0+=>x=-1
since we have rectangle, we need only positive solution; sox=4