Cynthia besch wants to buy a rug for a room that is 19 ft wide and 32 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 420 square feet of carpeting. what dimensions should the rug have?

The rug should be 15 ft wide and 28 ft long.

Step-by-step explanation:

I have attached a figure that represents the situation.

The the rug is by , the width of the strip of floor is .

We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that

(this says the area of the rug must be 420 square feet)

From the figure we see that

Therefore,

We expand this equation and get:

using the quadratic equation we get two solutions:

since the second solution, namely , is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take to be our solution.

Now we find the dimensions of the rug:

The rug is 15 ft wide and 28 ft long.

answer: add the !

step-by-step explanation: then we will answer