A rectangle and a square have the same area. The width of the rectangle is 2 in less than the side of the square and the length of the rectangle is 3 in less than twice the side of the square. What are the dimensions of the rectangle?

The area of a rectangle is A=LW, the area of a square is A=S^2.

W=S-2 and L=2S-3

And we are told that the areas of each figure are the same.

S^2=LW, using L and W found above we have:

S^2 = (2S-3) (S-2) perform indicated multiplication on right side

S^2=2S^2-4S-3S+6 combine like terms on right side

S^2=2S^2-7S+6 subtract S^2 from both sides

S^2-7S+6=0 factor:

S^2-S-6S+6=0

S (S-1) - 6 (S-1) = 0

(S-6) (S-1) = 0, since W=S-2, and W>0, S>2 so:

S=6 is the only valid value for S. Now we can find the dimensions of the rectangle ...

W=S-2 and L=2S-3 given that S=6 in

W=4 in and L=9 in

So the width of the rectangle is 4 inches and the length of the rectangle is 9 inches.