Question

The side of a square has the length (x-2), while a rectangle has a length of (x-3) and a width of (x+4). If the area of the rectangle is twice the area of the square, what is the sum of the possible values of x? I CAN'T ACCESS A FILE SO PLEASE JUST LOOK AT THE PICTURE YOURSELF, AND THEN TELL ME. THANKS!

Answer 1

Sum = 4 + 5 = 9

Explanation:

Equation

2*(x - 2)(x-2) = (x - 3)(x + 4)

Solution

2*(x^2 - 4x + 4) = x^2 + 4x - 3x - 12

2x^2 - 8x + 8 = x^2 +x - 12 Subtract the right side from the left

x^2 - 9x + 20 = 0

(x - 4)(x - 5) = 0

The possible values for x are

x - 4 = 0

x = 4

x - 5 = 0

x = 5

Check

(4 - 2)^2 = (4) = 4

(x - 3)(x + 4) = (4 - 3)(8) = 8

This checks

(5 - 2)^2 = 3^2 = 9

(5 - 3)(5 + 4) = 2 * 9 = 18