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How to find area and side length of triangle?

2 questions i cant figure out ?

1. Find the side length of an equilateral triangle with an area of 36sqrt3

2. Find the perimeter of an equilateral triangle with a height of 7sqrt3.

please explain or give formulas or even a website that explains? thanks

The area of a triangle is bh/2. An equilateral triangle has some special properties that help us out.
Slice the equilateral triangle down the middle vertically, producing 2 30/60/90 degree triangles. If the base of the 30/60/90 triangle is x, then the hypotenuse (the original side of the triangle) is 2x, and the height is Sqrt(3)x. so the area of the equilateral triangle is the same as both of the 30/60/90 triangles, or x^2 Sqrt(3) where x is half the side of the equilateral triangle.

So x = 6 and the side of the equilateral triangle is 12.

2) If the height is 7sqrt(3) then teh base of teh 30/60/90 is 7, and the side is 14. 3 x 14 = 42

Grandpa

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2 Responses to “How to find area and side length of triangle?”

  1. i would use the law the cosine: to get your answers and know that a equalateral triangle must have its lenghts and angles equal to one another.
    another thing you can do is split the triangle in half, which means the base of your new triable if half the base of the old one. Then you can use pathagorean theorem to get the other two sides.

    PS by the way the angle is of the equalterial triangle is 180/3 which is 60 degrees.
    Wikipedia has the equations and explanations you need.

    c^2= (a^2)+(b^2)cosY
    References :

  2. The area of a triangle is bh/2. An equilateral triangle has some special properties that help us out.
    Slice the equilateral triangle down the middle vertically, producing 2 30/60/90 degree triangles. If the base of the 30/60/90 triangle is x, then the hypotenuse (the original side of the triangle) is 2x, and the height is Sqrt(3)x. so the area of the equilateral triangle is the same as both of the 30/60/90 triangles, or x^2 Sqrt(3) where x is half the side of the equilateral triangle.

    So x = 6 and the side of the equilateral triangle is 12.

    2) If the height is 7sqrt(3) then teh base of teh 30/60/90 is 7, and the side is 14. 3 x 14 = 42

    Grandpa
    References :

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