# SOLUTION: The length of a rectangular floor is 3 meters less than three times its width. If a diagonal of the rectangle is 13 meters, find the length and width of the floor.

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Question 628789: The length of a rectangular floor is 3 meters less than three times its width. If a diagonal of the rectangle is 13 meters, find the length and width of the floor.
Answer by graphmatics(170)   (Show Source):
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Let w be the width of the rectangle. Then the length of the rectangle is given by 3w-3. For a right triangle with diagonal c and sides a and b c*c=a*a+b*b. So for this rectangle with a diagonal of 13 meters. 13*13=w*w+(3w-3)*(3w-3) 169=w*w+9*w*w-18w+9 10*w*w-18*w-160=0
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=6724 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5, -3.2. Here's your graph:

So if the width is 5 the length is 12.