Posted by **Joe** on Tuesday, July 12, 2011 at 7:11pm.

The altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 1500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9500 centimeters and the area is 87000 square centimeters?

- Calculus -
**Damon**, Tuesday, July 12, 2011 at 7:17pm
A = .5 b h

so

87,000 = .5 b (9500)

b = 18.32

then calculus

dA/dt = .5 (b dh/dt + h db/dt)

1500 = .5 ( 18.32 * 3000 + 9500 * db/dt)

- Calculus -
**Reiny**, Tuesday, July 12, 2011 at 7:22pm
strange .....

http://www.jiskha.com/display.cgi?id=1310504428

- Calculus -
**Joe**, Tuesday, July 12, 2011 at 7:24pm
-13.67?? ...

- Calculus -
**Damon**, Tuesday, July 12, 2011 at 7:33pm
I got -5.47

If the base were constant the area would be increasing faster than 1500cm^2/min due to the rapid altitude increase. Therefore the base must be decreasing.

- Calculus -
**Joe**, Tuesday, July 12, 2011 at 7:36pm
positive 5.47

- Calculus -
**Damon**, Tuesday, July 12, 2011 at 8:11pm
1500 = .5 ( 18.32 * 3000 + 9500 * db/dt)

3000 = 54960 + 9500 db/dt

9500 db/dt = -51,960

db/dt = -5.47

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