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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?

Respuesta :

Answer:

At that moment dB/dt=0

Step-by-step explanation:

The area of a triangle is given by

A=bh/2

A=area, b=base, h=height

If we differentiate over time:

[tex]\frac{dA}{dt} =\frac{dB}{dt}\frac{H}{2}  +\frac{dH}{dt}\frac{B}{2}[/tex] (product differentiation)

we have that:

[tex]\frac{dH}{dt}=2.5 cm/m[/tex]

[tex]\frac{dA}{dt}=1.5 sqcm/m[/tex]

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

[tex]84=\frac{8B}{2}[/tex]

[tex]B=21[/tex]

Therefore

[tex]84 =\frac{dB}{dt}\frac{8}{2}  +8*\frac{21}{2}[/tex]

[tex]\frac{dB}{dt}=0[/tex]

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