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?

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- Jul 22nd 2007, 12:25 PM #1

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- Jul 22nd 2007, 12:41 PM #2
Let $\displaystyle x$ be the width of the strip around the rug.

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

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

Since $\displaystyle x$ is the width of the strip:

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

so we must have:

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

can you take it from here?

- Jul 22nd 2007, 12:51 PM #3

- Jul 22nd 2007, 01:02 PM #4

- Jul 22nd 2007, 01:21 PM #5