The length of a rectangular table is 1 foot more than twice the length of a side of a square rug and the width of the table is 3 feet less than the length of a side of the rug. if the area of the table is 81 ft squared greater than the area of the rug, what is the area of the rug?

Let us assume the length of a side of a square rug = x

Then

Length of the rectangular table = (2x + 1) feet

Width of the rectangular table = (x - 3) feet

Area of the square rug = (Side) ^2

= x^2

Area of the rectangular table = (x^2 + 81) square feet

Now

Area of the rectangular table = Length * Width

x^2 + 81 = (2x + 1) * (x - 3)

x^2 + 81 = 2x^2 - 6x + x - 3

x^2 + 81 = 2x^2 - 5x - 3

2x^2 - x^2 - 5x = 81 + 3

x^2 - 5x = 84

x^2 - 5x - 84 = 0

Now we can solve this equation by factoring method and we will get

(x + 7) (x - 12) = 0

As x cannot be negative. so

x - 12 = 0

x = 12

Then

Area of the rug = x^2

= (12) ^2

= 144 square feet

So the area of the rug is 144 square feet.