Answer:
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
