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Finding perimeter of an equilateral triangle with only area given?

Really confused. If the area of an equilateral triangle is 16 radical 3, how do you find the perimeter? I know you have to use the 30-60-90 triangle theorem, but that’s about it. I’m really confused. Please help!

use the 30-60-90 triangle theorem
the ratio of the shorter leg: hypotenuse:longer leg
= 1:2:√3

Let the side of the equilateral triangle be 2x and the base of
the triangle also = 2x. Then the altitude = √3 x

The area = base * height ÷ 2
= 2x * √3 x ÷ 2
= x² √3

If the area of an equilateral triangle is 16 radical 3,
16 √3 = x² √3
x = 4
Base and the sides are 2x = 8
Perimeter = 8* 3 = 24

This entry was posted on Monday, December 28th, 2009 at 7:31 pm and is filed under triangle area. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “Finding perimeter of an equilateral triangle with only area given?”

  1. use the 30-60-90 triangle theorem
    the ratio of the shorter leg: hypotenuse:longer leg
    = 1:2:√3

    Let the side of the equilateral triangle be 2x and the base of
    the triangle also = 2x. Then the altitude = √3 x

    The area = base * height ÷ 2
    = 2x * √3 x ÷ 2
    = x² √3

    If the area of an equilateral triangle is 16 radical 3,
    16 √3 = x² √3
    x = 4
    Base and the sides are 2x = 8
    Perimeter = 8* 3 = 24
    References :

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