a 4 foot by 6 foot rug covers half of the area of a room leaving a uniform strip of bare floor around the edges. what are the dimensions of the room?

Question

im having trouble figuring out the answer

Answer 1

You can do this by Algebra.

 

If rug area equals 4•6=24, then entire area = 48. 

 

Now, the uniform strip of width x around the rug means that the overall dimensions (room) must be 4+2x and 6+2x and this product equals 48.

 

So (6+2x)(4+2x) = 48. 

 

Solve this by first dividing both sides by 4, then FOILing the left side, and subtracting the right-side constant from both sides, getting (3+x)(2+x) = 12;

 

x²+5x-6 = 0, (x+6)(x-1) = 0, x = 1 (reject x = -6 in this case).