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divide the square into four

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divide the square into four

by sanju09 » Tue Feb 23, 2010 4:38 am
The diagonals of square ABCD of area 4 divide the square into four non -overlapping triangles. What is the sum of the perimeters of those triangles?
(A) 4 (1 + √2)
(B) 4 (2 + √2)
(C) 8 (1 + √2)
(D) 8 (2 + √2)
(E) 4 (4 + 3 √2)
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by firdaus117 » Tue Feb 23, 2010 4:45 am
Each side=2
Each diagonal=2 sqrt(2)
Perimeter=4*2+2*2*sqrt(2)
Option B
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by harsh.champ » Tue Feb 23, 2010 4:48 am
sanju09 wrote:The diagonals of square ABCD of area 4 divide the square into four non -overlapping triangles. What is the sum of the perimeters of those triangles?
(A) 4 (1 + √2)
(B) 4 (2 + √2)
(C) 8 (1 + √2)
(D) 8 (2 + √2)
(E) 4 (4 + 3 √2)
Area of each triangle =1
Diagonals of squares intersect at <90 degrees.
SO,area of each triangle = 1/2 x (length of diagonal/2) x (length of diagonal/2)
Perimeter of 1 triangle = (√2) +(√2) + 2
=2(1 + √2)
Hence, for 4 triangles =[spoiler] 8(1 + √2)
C ans.[/spoiler]
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by harsh.champ » Tue Feb 23, 2010 4:50 am
firdaus117 wrote:Each side=2
Each diagonal=2 sqrt(2)
Perimeter=4*2+2*2*sqrt(2)
Option B
Hey you made a mistake over here.
C would be the answer.
Consider all the triangles-you missed out on the diagonals
We have to consider the diagonals twice.
This was the trap in the ques. :)
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by firdaus117 » Tue Feb 23, 2010 4:51 am
firdaus117 wrote:Each side=2
Each diagonal=2 sqrt(2)
Perimeter=4*2+2*2*sqrt(2)
Option B
Silly me!!! :oops:
Morale of the story:Utilize all 75 minutes of GMAT maths section.Even on seemingly easier questions,we should double check through figures.
Last edited by firdaus117 on Tue Feb 23, 2010 4:53 am, edited 1 time in total.
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by Pedros » Tue Feb 23, 2010 4:52 am
is it C ?

the 2 digonals counted twice plus the bases of the 4 triangles

so 4 * 2*(root 2) + 8 =
8(root 2) + 8 =

8 * ( 1 + (root 2 ) )
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by harsh.champ » Tue Feb 23, 2010 4:57 am
firdaus117 wrote:
firdaus117 wrote:Each side=2
Each diagonal=2 sqrt(2)
Perimeter=4*2+2*2*sqrt(2)
Option B
Silly me!!! :oops:
Morale of the story:Utilize all 75 minutes of GMAT maths section.Even on seemingly easier questions,we should double check through figures.
You fell into the trap
Good moral .
It should be religiously followed.
Hey you know what,while I was solving the problem ,your answer was posted and when I was writing this post u again edited and posted the morale-gud gud nice speed on the board.
Neways,we get suff. break time to refresh ourselves in the GMAT

Pedros wrote:is it C ?

the 2 digonals counted twice plus the bases of the 4 triangles

so 4 * 2*(root 2) + 8 =
8(root 2) + 8 =

8 * ( 1 + (root 2 ) )
Yes,Pedro the answer is C.
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