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# In the figure above, line AC represents a seesaw that is

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Director
Joined: 09 Aug 2006
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In the figure above, line AC represents a seesaw that is [#permalink]

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07 Jun 2007, 20:48
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20. In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C?

(1) x = 30
(2) Point B is 5 feet above the ground.
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VP
Joined: 08 Jun 2005
Posts: 1144

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07 Jun 2007, 23:32

two triangles are similar if:

a) 3 angles of 1 triangle are the same as 3 angles of the other.

or b) 3 pairs of corresponding sides are in the same ratio

or c) An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio.

since we can know that we are dealing with similar triangles based on a).

we can tell the height of C, from statement 2 alone.

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SVP
Joined: 01 May 2006
Posts: 1794

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07 Jun 2007, 23:36
(B) too

Theorem of Thales

Let B' and C' be the perpendicular projections of B and C.

We have so:
AB/AC = BB'/CC'
<=> 1/2 = 5/CC' as AC=2*AB
<=> CC' = 10

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07 Jun 2007, 23:36
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