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joyseychow
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2 triangles 09 Jun 2009, 07:41
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Pls. explain. Thks!



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2 triangles 09 Jun 2009, 08:23
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Attachment:
solution.jpg
solution.jpg [ 13.46 KiB | Viewed 1569 times ]

These are similar triangles. Similar triangles have sides in the same ratio.
let height of triangles be h and H

Now, for smaller triangle, side s corresponds to height h
implies, side S corresponds to height H = h/s * S

Area of small triangle = 1/2*s*h
Area of larger triangle = 1/2*S*H = 1/2 *S* (h/s *S)

Given area of larger is twice area of smaller, hence
1/2 *S* (h/s *S) = 2 * (1/2 * s*h) --- solve this
or, S = s√2

Answer C
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2 triangles 09 Jun 2009, 10:18
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agree to the above explanation. The answer is C.
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mdfrahim
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2 triangles 10 Jun 2009, 20:27
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Since both triangles are similar , it does not matter what are the values of angles X,Y,Z.I assumed all to be 60 so it becomes an equilateral triangle.
Area of small triangle ,A1= (sqrt(3)s^2)/4
Area of Large triangle,A2 = (sqrt(3)S^2)/4
According to question,
A2 = 2A1
which easily gives S=sqrt(2)s

I followed this approach to avoiad calculating height (unnecessary calculation)



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