Question

The altitude of a triangle is increasing at a rate of 2.5 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 1.5 1.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8 8 centimeters and the area is 84 84 square centimeters?

Answer 1

At that moment dB/dt=0

Explanation:

The area of a triangle is given by

A=bh/2

A=area, b=base, h=height

If we differentiate over time:

`(dA)/(dt) =(dB)/(dt)(H)/(2)  +(dH)/(dt)(B)/(2)` (product differentiation)

we have that:

`(dH)/(dt)=2.5 cm/m`

`(dA)/(dt)=1.5 sqcm/m`

When H=8 and A=84 then B is equal to

`84=(8B)/(2)`

`B=21`

Therefore

`84 =(dB)/(dt)(8)/(2)  +8*(21)/(2)`

`(dB)/(dt)=0`