Geometry Word Problem

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Geometry Word Problem

by rtaha2412 » Mon Nov 08, 2010 1:01 pm
Hey all. I am struggling interpreting this word problem so any assistance will be greatly appreciated.

A rectangular floor is covered by a rug except for a strip p meters wide along each of the four edge. If the floor is m meters by n meters, what is the area of the rug in square meters?

A) mn-p(m+n)
B) mn-2p(m+n)
C) mn-p^2
D) (m-p)(n-2p)
E) (m-2p)(n-2p)
Source: — Problem Solving |

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by MAAJ » Mon Nov 08, 2010 2:11 pm
This one is pretty easy:

You know that the area of a rectagle is base * height, in this case its: N * M

We want to know the area of the rug which is smaller than the area of the floor. Looking at the picture we can see that:

The base of the rug is N - P - P = N - 2P
The height of the rug is M - P - P = M - 2P

Thus, the area of the rug should be: (N-2P)(M-2P)

Correct Answer (E)
Attachments
rug.JPG