Answer:
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!
