I'm not sure about this one. I don't know the width to length ratio, so how do I do this? It just says that the length is more than 2 inches long. By how much?

Question

556.A rectangle is 2 inches wide, and more than 2 inches long. It so happens that this rectangle can be divided, by a single cut, into a 2-inch square and a small rectangle that has exactly the same shape as the large rectangle. What is the length of the large rectangle?

Answer 1

Draw and label a diagram. A 2 by 2 sqaure attached to a 2 by x rectangle

The snall rectangle is similar to the large rectangle

2 / x = (2 + x) / 2

4 = x(2 + x)

4 = 2x + x²

0 = x² + 2x - 4

Use the Quadratic Formula to solve for x.