An equilateral triangle has an area of 9 radical 3 square inches. how many inches is the perimeter?

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inches-perimeter

#1

An equilateral triangle has an area of 9 radical 3 square inches. how many inches is the perimeter?

Answer:

The altitude divides the triangle into two 30-60-90 triangles. The short leg is ½ the base, or b/2. So, the altitude is b√3/2. Area of full triangle is half base times height so:

A=(b/2)*(b√3/2)=(b²√3)/4 = 9√3

That means b²/4 = 9
b²=36
b=6

Perimeter is 3b =3*6 = 18 inches