Question

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2cm2 /min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2 ?

Answer 1

We have the area of the triangle
`A(t)= (bh)/(2)`.

`b=(2A)/(h)`

Differentiating with respect to time t,

`(db)/(dt)=(d)/(dt)((2A)/(h) )`

`(db)/(dt)=((2)/(h) )(dA)/(dt)-((2A)/(h^2) )(dh)/(dt)`

Substituting numerical values, the rate of change of base length is

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