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What is a function that models the area of an equilateral triangle in terms of the length #x# of ones of its sides?

Answer 1

Maverick Smith

#f(x) = x^2 sqrt 3 / 4#

#Delta ABC# is equilateral. #|CH| = h = x sin 30º#

#A_Delta = (hx)/2 = 1/2 * sin frac{pi}{6} * x^2 = f(x)#

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Answer 2

James Atkins

The function that models the area ( A ) of an equilateral triangle in terms of the length ( x ) of one of its sides is:

[ A(x) = \frac{\sqrt{3}}{4}x^2 ]

where ( x ) is the length of one of the sides of the equilateral triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.