Lets say:
height of small triangle = h
height of big triangle = H
we know that:
base of small triangle = s
base of big triangle = S
Area of big triangle = 2 x Area of small triangle
(1/2)*H*S = 2*(1/2)*h*s
Since both triangles are similar (their internal angles are identical), the ratio of the corresponding lengths must be equal:
s/S = h/H
So,
(1/2)*H*S = 2*(1/2)*h*s
H*S = 2*h*s
S = 2*s*(h/H)
S = 2*s*(s/S)
S^2 = 2*(s^2)
S = (√2)*s
Choose C.
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Gmat prep similar triangles
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bluementor
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bluementor wrote:Lets say:
height of small triangle = h
height of big triangle = H
we know that:
base of small triangle = s
base of big triangle = S
Area of big triangle = 2 x Area of small triangle
(1/2)*H*S = 2*(1/2)*h*s
Since both triangles are similar (their internal angles are identical), the ratio of the corresponding lengths must be equal:
s/S = h/H
So,
(1/2)*H*S = 2*(1/2)*h*s
H*S = 2*h*s
S = 2*s*(h/H)
S = 2*s*(s/S)
S^2 = 2*(s^2)
S = (√2)*s
Choose C.
-BM-
