SOLUTION: The lenght of an altitude of a triangle is one-third the lenght of the side to which it is drawn. If the area of the triangle is 6 square centimeters, find the lenght of that attit

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Question 138181: The lenght of an altitude of a triangle is one-third the lenght of the side to which it is drawn. If the area of the triangle is 6 square centimeters, find the lenght of that attitude?
Answer by solver91311(24713) About Me  (Show Source):
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The area of a triangle is A=%281%2F2%29bh where b is the base and h is the height or altitude. The base is that side of the triangle to which the altitude is drawn.

So, if x is the altitude then 3x is the base because the length of the altitute is one third the length of the base.

Substituting in the area formula: %281%2F2%29%283x%29%28x%29=6

%281%2F2%293x%5E2=6

%281%2F2%29x%5E2=2

x%5E2=4

x=sqrt%284%29=2 (ignore the negative square root because we are calculating a length)

So, the altitude is 2.

Check the answer:

A=%281%2F2%29bh

b=3h=3%2A2=6, so

A=%281%2F2%29%286%29%282%29=6 Answer checks.