geometry

[naaga]

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)


folks plz explain standard method for this kind of problems

thanks in advance

[DanaJ]

You basically have two rectangles:
a. the bigger rectangle is the floor with a surface of m*n
b. the smaller rectangle is the rug. The are of this one is (are of floor) - (area not covered by the rug).
The are not covered by the rug will be 2*p*n + 2*(m - 2p)*p. This means that the surface of the rug will be mn - 2pn - 2pm + 4p^2 = (mn - 2pm) - (2pn - 4p^2) = m(n - 2p) - 2p(n - 2p) = (m - 2p)(n - 2p).

Another way of solving this is considering length of rug = x and width of rug = y. Then x = m - 2p (since you've got a strip of p length on the right and one on the left) and y = n - 2p (since you 've got a strip of p length on the top and one on the bottom). This makes area = (m - 2p)(n - 2p). This method is slightly faster.

My guess is E.

[anishprabhu]

Answer is E

[naaga]

thankyou Danaj, excellent explanation