The altitude of a triangle is increasing at a rate of 2000 centimeters/minute wh

Question

The altitude of a triangle is increasing at a rate of 2000 centimeters/minute while the area of the triangle is increasing at a rate of 3000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 90000 square centimeters? Note: The "altitude" is the "height" of the triangle in the formula "Area=(1/2)*base*height". Draw yourself a general "representative" triangle and label the base one variable and the altitude (height) another variable. Note that to solve this problem you don't need to know how big nor what shape the triangle really is.

Explanation / Answer

A = 1/2 * b * h

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

given dA/dt = 3

dh /dt = 2

h = 10

A = 90

from the formula A = 1/2 b * h , we get b = 18

put these in the equation to get

db/dt = -3 cm / min

so the base is decreasing at 3 cm /min

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