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Calculus/related rates of a triangle

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Expert: - 10/15/2010


Question
A triangle's Height is growing at 2.5cm/min while its area is
growing at 7cm^2/min. At what rate is the base growing when
the area is 42 cm^2 and the height is 18 cm  

Answer
When the area of a triangle is 42 cm^2 and the height is 18 cm,
that means  A = bh/2 with b as base and h as height that h = 18 cm.

Putting these two values in gives 42 = b(9), so b = 42/9 = 14/3.

Now in this problem, we really have A(t) = b(t)h(t)/2.
Taking the derivative gives A'(t) = [b'(t)h(t) + b(t)h'(t)]/2.

We are given A'(t) = 72 cm^2/min, h(t) = 18 cm, b(t) = 14/3 cm, and
h'(t) = 2.5 cm/min.

Putting these values into the equation leaves b'(t) as the unknown variables with all of the other terms known.  Once this has been done, b'(t) can be solved for to find out what it's value is.

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