The perimeter of a rectangular rug is 24 ft. The length of the rug is 1 2/5 its width. What is the area of the rug?

35 ft²

Step-by-step explanation:

We set up a system of linear equations describing this rug and then solve it:

Perimeter: P = 2L + 2W

L = (1 2/5) W = 1.4W

Going back to the Perimeter equation, and knowing that P here is 24 ft, we have:

24 ft = 2 (1.4W) + 2W, or 2.8W + 2W, or 4.8W.

Solve for W (width) by dividing both sides of this equation by 4.8:

W = 24 ft / 4.8 = 5

The width of the rug is 5 ft; the length is 1.4 (5 ft), or 7 ft.

Thus the area of the rug is A = L * W, or A = (7 ft) (5 ft) = 35 ft²