Cynthia besch wants to buy a rug for a room that is 1313 ft wide and 2222 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 112112 square feet of carpeting. what dimensions should the rug have?

Alright, so if the uniform strip is x feet long, (1313-x) represents the width of the rug and 2222-x represents the length of the rug (given that the uniform strip is uniform all around the room) due to that the difference between the length of the room and the uniform strip is the rug because there is nothing else on the floor.

Since the area is 112112 square feet, we get that (1313-x) * (2222-x) is the area of the rug which equals 112112. Multiplying it out, we get

x^2-2222x-1313x + (1313*2222) = 112112. Next, we get

x^2-3535x+2917486=112112, and we subtract 112112 from both sides to get x^2-3535x+2805374=0. Using the quadratic formula, we get

(3535+-sqrt (3535^2-4*2805374)) / 2=either around 2332 or 1203. Since it can't be 2332 due to that 1313 is less than that and the rug cannot be negative in width, we get 1203 as the uniform width.

The dimensions of the rug are 1313-1203=around 110 as the width and 2222-1203=around 119 feet