SOLUTION: a room's length is 3 feet less than twice its width. the area if the room is 135 square feet. What are the rooms dimensions?

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Question 153149: a room's length is 3 feet less than twice its width. the area if the room is 135 square feet. What are the rooms dimensions?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width of the room, then the length can be expressed in terms of x as 2x - 3.
Its area in terms of x is x(2x - 3).
Setting x(2x - 3) = 135, we have
x(2x - 3) = 135
Re-arrange the quadratic equation into standard form:
2x^2 - 3x - 135 = 0
Solve it by using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Here a = 2, b = -3 and c = -135
So
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-135%29+%29%29%2F%282%2A2%29+
=%283+%2B-+sqrt%28+9%2B1080+%29%29%2F4
=%283+%2B-+sqrt%28+1089%29%29%2F4
=%283+%2B-+33%29%2F4
So x+=+%283%2B33%29%2F4+=+36%2F4=9 or x+=+%283-33%29%2F4+=+-30%2F4=-7.5
Reject x = -7.5 as the width can not be negative.
So the solution is x = 9
Therefore the width is 9ft,the length is 2x - 3=2*9-3=15.