Question

We are interested in the dimensions of a certain rectangle. This rectangle has length triple the side of the square and width two units less than the side of the square. If the two areas are equal, what are the rectangle's dimensions (w x h)?

Answer 1

Let s be the side of the square. The length of the rectangle is 3s and its width is equal to s - 2. From the given condition,
                              A (square) = A (rectangle)
                                 s² = (3s)(s - 2)
                                 s² = 3s² - 6s
                                   -2s² = -6s
                                       s = 3
Thus, the length of the rectangle is 9 and its width is 1