The sides of an equilateral triangle are increasing at a rate of 5 cm/min . At what rate is the area of the triangle increasing when the sides are 20 cm long?

Answer 1

An equilateral triangle with sides "s" has an altitude (height) of s√3/2 like this:

The area is 1/2bh = 1/2(s)(s√3/2) = s²√3/4

If A = s²√3/4 then, differentiating with respect to time:gives us:

dA/dt = 2s√3/4•ds/dt (using the chain rule). Simplifying:

dA/dt = s√3/2•ds/dt

When s = 2 and ds/dt = 5 cm/min then:

dA/dt = (2)√3/2•(5) = 5√3 cm²/min (which is approximately 8.66 cm²/min)

Answer 2

Write down the formula for the area of an equilateral triangle (in case you have forgotten, it's A = (1/2)bh ).

Differentiate both sides of the formula with respect to time.

Plug in the numbers and do the arithmetic.