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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?

1 Answer

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Answer:

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

User Mightyhal
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