Posted by **Amy** on Tuesday, October 15, 2013 at 10:45pm.

The height of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 square cm/min. At what rate is the base of the triangle changing when the height is 7 centimeters and the area is 91 square centimeters?

- Calculus Practice Problems -
**Reiny**, Tuesday, October 15, 2013 at 11:03pm
A = (1/2) b h

dA/dt = (1/2)(b dh/dt + h db/dt)

given: dA/dt = 2 , dh/dt = 1 , A = 91 , h = 7 ,

we need the base b,

from A = 1/2)bh

91 = (1/2)(7b)

182 = 7b

b = 26

2 = (1/2)(26(1) + 7db/dt)

4 = 23 + 7db/dt

db/dt = -19/7 cm/min

At that moment, the base is decreasing at 19/7 cm/min

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