Question

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

Answer 1

You 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 right-angled 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, \[a=\sqrt{300}=10\sqrt{3}\]

Answer 2

The a/2 in the first step comes from the fact that the altitude dropped from the apex bisects the base.

Answer 3

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