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Rufina [12.5K]
3 years ago
11

The altitude of an equilateral triangle is 5 cm. what is the length of a side of the triangle?

Mathematics
1 answer:
Grace [21]3 years ago
3 0

Answer:

The length side of the triangle is \frac{10\sqrt{3}}{3}\ cm

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal internal angles of measure of 60 degrees each.

Let

b------> the length side of the equilateral triangle

Applying Pythagoras theorem

b^{2}=(b/2)^{2}+5^{2}\\\\ b^{2}-(b/2)^{2}=25\\\\ (3/4)b^{2}=25\\ \\b^{2} =25*4/3\\ \\b=\frac{10}{\sqrt{3}}\ cm\\ \\b=\frac{10\sqrt{3}}{3}\ cm

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