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Side: 10

Perimeter: 30

Step-by-step explanation:

An equilateral triangle has a height of 5√3. What is the length of each side in the equilateral triangle? What is the perimeter of the equilateral triangle?

In triangles with angles with 30°, 60°, and 90°, the hypotenuse (the angle opposite to the 90° angle) is twice as long as the base, and the height is √3 times as long as the base. To make it easier, this is a list of the sides:

x = base

√3 * x = height

2x = hypotenuse.

Look at the drawing I have attached below

If AD is the base of the triangle ADC, then CD, the height is √3 times AD. If we set AD as x, CD = √3*x = 5√3

√3*x = 5√3

Divide both sides by √3.

x = 5

Then, because altitudes in equilateral triangles bisect the base (CD cuts AB in half), then AB = 10.

The sides in equilateral triangles are equal, so each side is 10.

Then, the perimeter must be 30.

I hope this helps! Feel free to ask any questions!

56

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