SOLUTION: The area of an equilateral triangle is 16 (square root) 3 square units. Find the altitude.

Question 290404: The area of an equilateral triangle is 16 (square root) 3 square units. Find the altitude.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The area of an equilateral triangle is 16(square root)3 square units. Find the altitude
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Area = (1/2)bh
16*sqrt(3) = (1/2)bh
bh = 32sqrt(3)
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Find b in terms of h
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Since the triangle is equilateral, all sides are "b":
Draw an altitude from the vertex to the base.
You have a right triangle with base = b/2 and hypotenuse = b
The altitude is the 3rd side:
b^2 = (b/2)^2 + h^2
h^2 = (3/4)b^2
b^2 = (4/3)h^2
b = (2/3)sqrt(3)h
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Substitute into bh = 32sqrt(3) and solve for "h":
(2/3)sqrt(3)h^2 = 32sqrt(3)
(2/3)h^2 = 32
h^2 = 96/2
h^2 = 48
h= 4sqrt(3)
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Cheers,
Stan H.
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