An isosceles triangle has a base that is 1.5 times the height. If the area is increasing at 9cm2/s, how fast is the height increasing when it is 12 cm high?

Known:
base=1.5H
dA/dt=9.0cm2/s
h=12cm
dh/dt= ?

Area for a triangle: LxW/2

After that, I am confused.

1 answer

ok, let's go with your definitions:

height: --- h
base --- 1.5h
area ---- a

given: d(a)/dt = 9 cm/s
find dh/dt, when h = 12
(I see variables a for area and h for height.
So I will need an equation that contains a and h)

a = (1/2)base x height
a = (1/2)(h)(1.5h) = .75h^2

d(a)/dt = 1.5h dh/dt
plug in our values
9 = 1.5(12)dh/dt = 18dh/dt

dh/dt = 9/18 = 1/2 cm/s

A common error is to use the given case of h=12 too soon.
You have to wait until you have found the derivative before subbing it in.