# Math Help - Just another question

1. ## Just another question

A floor measures 12m by 8m. A rug covers one-third of the floor. The uncovered part of the floor forms a uniform (same width) strip around the rug. How wide is the strip?

2. Originally Posted by zbest
A floor measures 12m by 8m. A rug covers one-third of the floor. The uncovered part of the floor forms a uniform (same width) strip around the rug. How wide is the strip?
Let $x$ be the width of the strip around the rug.

Note that the area of the floor is $12 \mbox { m} \times 8 \mbox { m } = 96 \mbox { m}^2$

If the rug covers 1/3 of the floor, it must have an area of $\frac {1}{3} 96 \mbox { m } = 32 \mbox { m}^2$

Since $x$ is the width of the strip:

The length of the rug is $(12 - 2x)$ and the width is $(8 - 2x)$, and the area (found above) is $32$

so we must have:

$(12 - 2x)(8 - 2x) = 32$

can you take it from here?

3. Here is a sketch for the solution of Jhevon.

4. Originally Posted by red_dog
Here is a sketch for the solution of Jhevon.
what did you use to draw that, red_dog?

5. I used Draw Tools from Word, then I imported to Irfanview and save it as an image.