Question

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.

Which equation can be used to solve for x, the increase in side length of the square in inches?

x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0

Answer 1

Let the new side be 4 + x. Then (4 + x)^2 = 81, so x^2 + 8x + 16 = 81 and x^2 + 8x - 65 = 0.

Answer: x^2 + 8x − 65 = 0.