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# The above rectangular box has a volume of 128 cubic inches.

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The above rectangular box has a volume of 128 cubic inches. [#permalink]  11 Aug 2006, 09:14
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The above rectangular box has a volume of 128 cubic inches. What is the area of triangle BED?

(1) The area of the square base is 16 square inches.
(2) |AB|=|BC|=2 inches
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triangle in box.doc [28 KiB]

Senior Manager
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IMO C

given - xyz=128

x - height
y - width
z - depth

S1 - yz=16

Therefore, x=8 Insuff

S2 - |AB| = |BC| = 2 inches

AC = 4 inches = y = z Insuff

S1&S2 - x=8, y=4 and z=4 Suff

Area is (1/2)bh

b = 4 = y

h = SQRT(8^2+4^2) = 4SQRT(5)

Area = 8SQRT(5)
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A

Assuming that
1. Point B is in the middle of AC because nothing like that is mentioned.
2. Figure is NOT drwan to scale

St1: If we know all sides then we can find the area. Even if B is not in the middle of AC, height of the triangle will remain the same.

Height of box = 128/16 = 8
Base of triangle = 4
Height of triangle = √80 = 4√5
Area = 8√5 : SUFF

St2: We don't know all the dimensions of the triangle. Other dimentions could be (4,8), (2,16) or (1,32): INSUFF
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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ps, from S1 how do you know the base is 4? It could be 2 or 8 as well right?
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agsfaltex wrote:
ps, from S1 how do you know the base is 4? It could be 2 or 8 as well right?

Its a square base..

go with (A).
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Man, I feel so stupid. Ofcourse its A.
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Consider A:
height of the solid = 128/Area(base) = 128/16 = 8
ABCD is a square, therefore AB = DE = 4
height of the triangle = length of diagonal CE <-- this is not very obvious
= sqrt(96)
area of triangle = 1/2 x diagonal x DE (SUFF)

Consider B:
AB = BC = 2. gives base 4, but no information about height. hence INSUFF

Ans: A
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