Please consider the following...?

Question

a room that has a rug in the middle, from the rug to the wall it is one foot on each side. the length is 2 ft longer than the width and the area of the rug is the same as the area of the room with the open space (the space around the rug). Question is, what are the dimensions of the room? Please don't post the actual answers, just post the method you use to solve it. Thanks! :)

Answer 1

length of the rug = L

width of the rug = W

area of the rug = (L)(W)

L = W+2

therefore, area of the rug = (W+2)(W) = W^2 + 2W

Since area of room is area of rug but with 1 foot longer in each direction (add on both sides so = 2)

therefore,

area of room = (L+2)(W+2) + (W+4)(W+2) = W^2 +6W + 8

since we know the area of the room is actually twice the size of the area of the rug:

W^2 + 6W + 8 = W^2 + 2W

which simplifies to:

W^2 - 2W - 8 = 0

which reduces to:

(W-4)(W+2) = 0

this has two real roots at W=4 and W=-2

We know that -2 cannot be true,

therefore,

W = 4, L = 6

and the dimensions of the room are therefore 2 feet larger than this at 6 by 8 feet!!

to confirm

area of rug = (4)(6) = 24

area of room = (6)(8) = 48

so its twice as big which is exactly what we want.

Good luck!

Answer 2

area of the rug is L x W.

area of the open space is 2 x L + 2 x W + 4

L = W + 2

So,

(W + 2) x W = 2 x (W + 2) + 2 x W + 4

Solve that.

Answer 3

wtf! im confused! omg.