Question

Ms. Sherman hired a contractor to lay a rectangular concrete patio in her backyard. The patio will be 12 feet wide and 18 feet long. She also asks the contractor to lay a separate concrete area, in the shape of a square, for a barbecue station. To stay within her budget, Ms. Sherman decides that the combined area of the patio and barbecue station will be approximately 300 square feet. Which equation can you use to find the length along each edge, x, of the barbecue station?

Answer 1

To find the length along each edge, x, of the barbecue station, set up the equation 216 + x^2 = 300 and solve for x. The length along each edge, x, of the barbecue station is approximately 9.165 feet.

Step-by-step explanation:

To find the length along each edge, x, of the barbecue station, we need to set up an equation based on the given information. Let the length of each side of the square barbecue station be x. The area of the patio is 12 feet wide and 18 feet long, so its area is 12 * 18 = 216 square feet. The combined area of the patio and barbecue station is 300 square feet, so we can set up the equation:

216 + x^2 = 300

To find the value of x, we can subtract 216 from both sides and then take the square root of both sides:

x^2 = 300 - 216

x^2 = 84

x = √84

The length along each edge, x, of the barbecue station is approximately 9.165 feet.