A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.

Question

(x + 5)x = 104

x2 + 5x – 104 = 0

Determine the solutions of the equation. What solution makes sense for the situation?

x =

What are the dimensions of the rectangle?

width =
inches

length =
inches

Answer 1

To solve the quadratic equation x^2 + 5x - 104 = 0, we can factor it or use the quadratic formula.

Factoring:
(x + 13)(x - 8) = 0
x = -13 or x = 8

Since the width cannot be negative, the only solution that makes sense for the situation is x = 8.

Therefore, the width of the rectangle is 8 inches.
The length of the rectangle is x + 5 = 8 + 5 = 13 inches.

So, the dimensions of the rectangle are:
Width = 8 inches
Length = 13 inches.