Question

The area of a rectangle is 52 in². The length of the rectangle is 9 in. longer than the width. What is the width of the rectangle?

3 in.
4 in.
6 in.
8 in.

Answer 1

Givens

Let the width = x

Let the length = x + 9

Area = 52 in^2

Formula

Area = L * W

Solve

52 = (x + 9)(x ) Remove the brackets.

52 = x^2 + 9x Subtract 52 from both sides

x^2 + 9x - 52 = 0 Factor

You need 2 numbers that add to 9 and multiply to 52. There aren't many

52 and 1

26 and 2

13 and 4

All three will multiply to 52. 52 = 52 + 1 or 52 - 1 (The larger number must be plus). 53 or 51 is not the sum. 52 and 1 is not the answer.

26 and 2 will add or subtract to 28 or 24. Neither 1 is 9. So that can't be your answer.

13 and 4 will give 9 or 17. There's your answer.

(x + 13)(x - 4) = 0

x = - 13 is not the answer. You cannot have minus distances.

x - 4 = 0

x = 4

The width is 4 inches <<<< answer.