A few days ago
Triangle Rate Problem- Please Help! =/?
The altitude of a triangle is increasing at a rate of 1.000 centimeters/minute while the area of the triangle is increasing at a rate of 1.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7.500 centimeters and the area is 90.000 square centimeters?
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Please show steps and reasoning.
Thanks for any help, hints, or suggestions. =)
Top 1 Answers
A few days ago
Favorite Answer
Let the base be b, the height (= length of altitude) be h and the area be A. These quantities can all be expressed as functions of time.
A = bh / 2 ………(1)
Differentiating with respect to time, and using the product rule:
dA/dt = (b dh/dt + h db/dt) / 2
2 dA/dt = b dh/dt + h db/dt
db/dt = (2 dA/dt – b dh/dt ) / h ……..(2)
dh/dt = 1000 cm / min
dA/dt = 1000 cm^2 / min
h = 7500 cm
A = 90000 cm^2
From (1)
b = 2A / h
= 2 * 90000 / 7500 cm
b = 24 cm.
Substituting these values in (2):
db/dt = (2*1000 – 24*1000) / 7500
= -220 / 75
= -2.93cm / min.
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