Question

A rectangular rug is placed on a rectangular floor. The width of the floor is 6 feet greater than the length, x, of the floor. The width of the rug is 4 feet less than the width of the floor. The length of the rug is 4 feet less than the width of the rug. Which function represents the area of the floor not covered by the rug?

Answer 1

To find the area of the floor not covered by the rug, we need to find the area of the floor and subtract the area of the rug. We can do this by setting up equations for the dimensions of the floor and the rug and then calculating the areas.

Step-by-step explanation:

To find the area of the floor not covered by the rug, we need to find the area of the floor and subtract the area of the rug. Let's start by finding the dimensions of the floor and the rug.

Given that the width of the floor is 6 feet greater than the length, and the width of the rug is 4 feet less than the width of the floor, we can set up the following equations:

Width of floor = length of floor + 6

Width of rug = width of floor - 4

Length of rug = width of rug - 4

Now, let's substitute the expressions for the dimensions of the rug into the equation for the area of the floor:

Area of floor = (length of floor)(width of floor)

Area of rug = (width of rug)(length of rug)

Finally, we can subtract the area of the rug from the area of the floor to find the area not covered by the rug.