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geometry

by rupsk » Thu Jul 28, 2011 8:17 am
A rectangle is such that it can be perfectly cut into smaller squares of a maximum possible side of length 12 units. It is also known that the perimeter of such a rectangle is 384 units.How many distinct rectangles are there which satisfy the criteria given?

A. 4
B. 8
C. 6
D. 5
E. 12
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by sharmishtha_goel » Thu Jul 28, 2011 9:16 am
8.
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by rupsk » Thu Jul 28, 2011 9:19 am
can you explain how you have reached to this number?
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by tryingtobeat » Thu Jul 28, 2011 9:34 am
Actually I misread the question. Distinct rectangles...
Last edited by tryingtobeat on Thu Jul 28, 2011 9:42 am, edited 3 times in total.
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by rupsk » Thu Jul 28, 2011 9:36 am
your answer is correct but I do not agree with the logic.
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by sharmishtha_goel » Thu Jul 28, 2011 12:04 pm
rupsk wrote:A rectangle is such that it can be perfectly cut into smaller squares of a maximum possible side of length 12 units. It is also known that the perimeter of such a rectangle is 384 units.How many distinct rectangles are there which satisfy the criteria given?

A. 4
B. 8
C. 6
D. 5
E. 12

Explaination:

2(l + w) = 384
l + w = 192

as each sq that is cut from it has a length of 12 , therefore both l and w should be multiples of 12.

l = 12a
w = 12b

12a + 12b = 192
12(a+ b)= 12*16
a+ b =16
dimensions of different rectangles : (15,1) (14,2) ..... you get 8 such rectangles.
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