find rate of change

Question

The base of a right triangle is half its height. If the base of the triangle is increasing at a rate of 2 cm/sec, find the rate of change of the area of the triangle when the base is 26cm.

Answer 1

All these problems you need to get a formula and use implicit differentiation and what you are given

 

in this case area of a triangle

A = (1/2)*b*h

objective: find dA/dt

given: b = 26, db/dt = 2, b = (1/2)*h

 

since we are given db/dt lets get area in terms of b

since b = (1/2)h that means h = 2b

 

so A = (1/2)*b*(2b) = b^2

Take derivative wrt time, t

dA/dt = 2b*db/dt

 

plug in values and done. Remember units. your answer will be cm^2/sec