Question

The altitude (i.e., height) of a triangle is increasing at a rate of 2.5 cm/minute while the area of the triangle is increasing at a rate of 2 square cm/minute. At what rate is the base of the triangle changing when the altitude is 7.5 centimeters and the area is 90 square centimeters?
The base is changing at_____ cm/min.

Answer 1

Refer to a solution using Mathematica for the calculations.

Answer 2

\[A = \frac{1}{2} b h\]
\[\frac{dA}{dt} =\frac{1}{2}(\frac{db}{dt} h + b \frac{dh}{dt})\]
solving for rate of base
\[\frac{db}{dt} = \frac{2 \frac{dA}{dt} - b \frac{dh}{dt}}{h}\]
Note
\[b = \frac{2A}{h}\]

Answer 3

thank you so much !