the perimeter of a standard-sized rectangular rug is 84 ft the length is 22 ft longer than the width find the dimensions

The length would be 32 and the width would be 10

Step-by-step explanation:

For the purpose of this, we'll set the width as x. We can then define the length as x + 22 since we know it is 22 ft longer than the width. Now we can use those along with the perimeter formula to solve for the width.

P = 2l + 2w

84 = 2 (x + 22) + 2 (x)

84 = 2x + 44 + 2x

84 = 4x + 44

40 = 4x

10 = x

Now since we know that the width is 10ft, we can add 22ft to it to get the length, which would be 32ft.