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Rug

by grandh01 » Fri Aug 03, 2012 3:28 pm
14. A rectangular floor is covered by a rug
except for a strip p meters wide along
each of the four edges. 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 - p2
(D) (m - p)(n - p)
(E) (m -2p)(n - 2p)
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by eagleeye » Fri Aug 03, 2012 4:23 pm
grandh01 wrote:14. A rectangular floor is covered by a rug
except for a strip p meters wide along
each of the four edges. 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 - p2
(D) (m - p)(n - p)
(E) (m -2p)(n - 2p)
let length of rug be x and width be y.
Since the uncovered strip is on all 4 sides,

For length, p+x+p = m => x= m-2p
For width, p+y+p = n => y = n-2p
Hence area of rug = xy =(m-2p)(n-2p) :)
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by truplayer256 » Fri Aug 03, 2012 4:50 pm
Note that if you visualize this, you'll see that:

Area of rug = Area of smaller rectangle within the rectangular floor.

Dimensions of smaller rectangle are (m - 2p) by (n - 2p)

Therefore the area is simply (m - 2p)(n - 2p)

Choose E
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