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.

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): You can put this solution on YOUR website!
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.
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