Question

A 15-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 7 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 9 feet from the wall?

Answer 1

pythagoras for this one

Answer 2

oh area! oops

Answer 3

\[A=\frac{1}{2}xy\]
\[A'=\frac{1}{2}\left(xy'+yx'\right)\]
you know \(x'=7\) so you need \(y'\)

Answer 4

still need pythagoras
you have
\[x^2+y^2=15\]
\[2xx'+2yy'=0\]
\[y'=-\frac{xx'}{y}\]
replace \(x'\) by \(7\) , \(x\) by \(9\) and \(y\) by \(12\) to find \(y'\) when \(x=9\), then replace in the equation above to find \(A'\)