Question

A rare square Turkish rug is sold at auction. The area of the Turkish rug in square feet is 396 more than its perimeter in feet. Find the length in feet of the side.

Answer 1

Answer:

  22 ft

Step-by-step explanation:

You want the length of one side of a square rug whose area in square feet is 396 more than its perimeter in feet.

Perimeter

If one side length is represented by s, then the perimeter of the square rug is ...

  P = 4s

Area

The area of that rug is the square of the side length:

  A = s²

Difference

The numerical difference between these values is given as 396, so we have ...

  s² -4s = 396

  s² -4s +4 = 400 . . . . . . . add 4 to complete the square

  (s-2)² = 400 . . . . . . . . . write as a square

  s -2 = 20 . . . . . . . . . . . positive square root

  s = 22 . . . . . . . . . . . . . add 2

The length of one side of the rug is 22 feet.