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Question

The height of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 2 square centimeters per minute. At what rate is the base of the triangle changing when the height is 11.5 centimeters and the area is 94 square centimeters?

using the formula for the area of a triangle:

Answer 1

Area = A = (1/2)bh, A=94 = (1/2)11.5b, b= 188/11.5

take the derivative of A, with respect to time

first term times derivative of the 2nd, plus 2nd term times derivative of the 1st term

A' = (1/2)bh' + (1/2)hb'

substitute A'=2, h'=3, b= 188/11.5, h=11.5

2 = (1/2)(188/11.5)(3) + (1/2)(11.5)b', solve for b'

4 = 564/11.5 + 11.5b'

b' = (4-564/11.5)/11.5 = -518/132.25 = about -3.9

b is decreasing at the rate of 3.9 cm per minute