A room's length is 3 feet less than twice its width. The area of the room is 135 sq feet. What are the room's dimensions?
Hope this helps:
A= L x W
135 = (2w-3)(W)
135 = (2w squared - 3W)
135 = 2w^2-3w
2w^2-3w-135 = 0
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Use the quadratic formula to get:
w = [3 +- sqrt(9 - 4*2*-135)]/4
Positive solution:
w = [3 + sqrt(1089)/4
w = [3 + 33]/4
w = 9 ft
L = 2W-3 = 2*9-3 = 15 ft.
If the width is w, the length is l = 2w-3.
The total area is length x width = w*(2w-3)
Solve
w*(2w-3)=135 to find w.
2w^2-3w-135=0
w = (3 +/- sqrt ( 9 +8*135))/4
The positive solution is
w = ( 3 + 33) /4 = 9 and then l = 15.
