Cynthia wants to buy a rug for a room that is 25 ft wide and 34 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 630 square feet of carpeting. What dimensions should the rug have?

30,23

What's the answer

To find the dimensions of the rug, we need to subtract the area of the room from the area of the rug with the uniform strip of floor.

Given:
Width of the room (W) = 25 ft
Length of the room (L) = 34 ft
Total carpeting area available (A) = 630 square feet

To calculate the area of the room, we multiply the width and length:
Area of the room = Width * Length = W * L = 25 ft * 34 ft = 850 square feet

Now, we subtract the area of the room from the total carpeting area to find the area of the rug with the uniform strip of floor:
Area of the rug = Total Carpeting Area - Area of the Room = A - Area of the room = 630 sq ft - 850 sq ft = -220 square feet

Uh-oh! It seems there's a problem with the given information. The area of the rug cannot be negative, so we may need to double-check the given values.

Please ensure that the measurements and the total carpeting area are correct.

so, if the rug has width w, to get the maximum 630 ft^2 of carpeting,

(25-2w)(34-2w) = 630
w = 2
So, the carpet is 2 ft wide.
Now, how long is it?