Question

the altitude of a triangle is increasing at a rate of 1 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 4 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10.5 10.5 centimeters and the area is 90 90 square centimeters?

Answer 1

-128/147 cm/min

Explanation:

`A=(1)/(2)bh \\ \\ 90=(1)/(2)(10.5)b \\ \\ b=(120)/(7) \\ \\ \\ A=(1)/(2) bh \\ \\ \implies (dA)/(dt)=(b)/(2) (dh)/(dt)+(h)/(2) (db)/(dt) \\ \\ 4=(21)/(4)+(db)/(dt)+(60)/(7) \\ \\ (db)/(dt)=-(128)/(147)`