Dimensions of a rug

Question

Zachary Daniels wants to buy a rug for a room that is 12 ft wide and 15 ft lon. He wants to leave a uniform strip of floor around the ru. He can afford to buy a 18ft^2 of carpetin. What dimensions should the rug have?

Answer 1

If we let the width and length of the rug be represented by x and y, we can set up two equations.

The first is that x*y=18, since that's all the rug he can afford.

The second equation comes from the uniform strip around the rug.  Since we want the distance to each wall to be the same from the sides of the rug, (12-x)/2 = (15-y)/2.  

Rearranging a bit we can solve this for y and then plug it into the first equation to obtain a quadratic equation which should factor nicely and give us the value of x.