Question

The length of a rectangle is x and the width is 2x-8. If the area of the rectangle is 234 yd^2, find the value of x.

Answer 1

x = 13

Explanation:

The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.

`A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x`

To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.

`2x^2 - 8x  - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\`

Set each factor equal to 0 and solve.

x - 13 = 0 so x = 13

x + 9 = 0 so x = -9

Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.