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anonymous
 5 years ago
I have an equilateral triangle with a altitude dropped. The altitude is 15 and I am trying to find the sides. Can anyone help?
anonymous
 5 years ago
I have an equilateral triangle with a altitude dropped. The altitude is 15 and I am trying to find the sides. Can anyone help?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to use Pythagoras' Theorem. The altitude can be dropped from the apex of the triangle from the base. If you do this, you'll see you end up with two congruent rightangled triangles. The sides of an equilateral triangle are all equal, so if you call the side length, a, then \[a^2=15^2+\left( \frac{a}{2} \right)^2 = 225+\frac{a^2}{4}\]That is\[a^2=225 + \frac{a^2}{4} \rightarrow 4a^2=900 +a^2 \rightarrow 3a^2=900 \]so\[a^2=\frac{900}{3}=300\]and therefore, \[a=\sqrt{300}=10\sqrt{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The a/2 in the first step comes from the fact that the altitude dropped from the apex bisects the base.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Feel free do give me a fan point ;p
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