Question

The altitude of a triangle is increasing at a rate of 2.0 centimeters/minute while the area of the triangle is increasing at a rate of 4.0 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.5 centimeters and the area is 84.0 square centimeters?

Answer 1

Area is \[A=\frac{1}{2}bh\] differentiating wrt time we get
\[A'=\frac{1}{2}(bh'+hb')\] via the product rule. now you are given that
\[A'=4\] and
\[h'=2\]
\[h=10.4\] and
\[A=84\]
solve for b, plug in the numbers to get your answer

Answer 2

or you can solve for
\[b'\] using algebra and then plug in the numbers. it is up to you

Answer 3

clear or no?

Answer 4

I get -2.315018315 as my answer, which is apparently incorrect.

Answer 5

or -1.523809524, which is also wrong.