a triangle has a base that is increasing

Question

A triangle has a base that is increasing at a rate of 1 cm/sec and a height that is decreasing at a rate of 4 cm/sec. Find the rate of change of the area of the triangle when the height is 4 cm and the area is 10 cm². Write your answer as a decimal rounded to two decimal places

Answer 1

A=hb/2

take the derivative with respect to time

A'A=(1/2)(hb'+h'b)

when A=10,h=4,b=5,h'=-4,b'=1

10A'=(1/2)((4)(1)+(-4)(5))

A'= -16/20

A'=-0.80 cm^2/sec