Question

A rectangular porch has dimensions of (x + 12) and (x + 5) feet. If the area of the porch floor is 120 square feet, what are its length and width?

Answer 1

The length of the porch is 15 feet and the width is 8 feet.

Step-by-step explanation:

To find the length and width of the porch, we need to set up an equation using the given information:

Area = length x width

120 = (x + 12)(x + 5)

Expanding the equation: 120 = x^2 + 17x + 60

Setting the equation equal to zero: x^2 + 17x - 60 = 0

Factoring the quadratic equation: (x + 20)(x - 3) = 0

Solving for x: x = -20, x = 3

Since the dimensions of the porch cannot be negative, we can conclude that x = 3.

Therefore, the length of the porch is x + 12 = 3 + 12 = 15 feet, and the width is x + 5 = 3 + 5 = 8 feet.