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# Triangle ABC and DEF are similar with their areas 9 sq. cm.

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Triangle ABC and DEF are similar with their areas 9 sq. cm. [#permalink]

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16 Aug 2004, 16:58
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Triangle ABC and DEF are similar with their areas 9 sq. cm. and 49 sq. cm. If the length of the median DN=7 cm, find the length of the median AM.
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16 Aug 2004, 17:15
smcgrath12 wrote:
Triangle ABC and DEF are similar with their areas 9 sq. cm. and 49 sq. cm. If the length of the median DN=7 cm, find the length of the median AM.

DN^2/AM^2 = Ar(DEF)/Ar(ABC)

49/AM^2 = 49/9

therefore AM must be 3.

Plz render the OA.
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16 Aug 2004, 17:16
Sorry, I am a newbie. What is OA?
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16 Aug 2004, 22:31
smcgrath12 wrote:
Sorry, I am a newbie. What is OA?

My question:
what is the median of a triangle? I don't understand the question....
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17 Aug 2004, 05:39
OA is 3.

A median of any triangle is a line segment drawn from a vertex to the opposite side in such a way that it bisects the opposite side. So basically you have 3 medians in any triangle. The intersection point of the 3 medians is called centroid and it always splits the medians into a 2:1 ratio.
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17 Aug 2004, 09:37
Just to make sure,
Are you squaring the medians because the areas are "sq. cm" ?
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17 Aug 2004, 09:49
Dookie wrote:
Just to make sure,
Are you squaring the medians because the areas are "sq. cm" ?

Yes, in similar triangles, the ratio of their areas is equal to ratio of the square of the length of any corresponding side. Also, the ratio of the medians in similar triangles is equal to the ratio of the length of any corresponding side. Voila, ratio of areas = sq. of corresponding medians.
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17 Aug 2004, 10:12
Thanks for clarifying.
17 Aug 2004, 10:12
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