The formula for the area of a triangle is
\(A=\frac{1}{2}bh\)
\(\rightarrow\frac{dA}{dt}=\frac{1}{2}(b\frac{dh}{dt}+h\frac{db}{dt})\)
We are given:
\(\frac{dh}{dt}=2\)
\(\frac{dA}{dt}=4.5\)
\(h=9.5\)
\(A=92\)
Plug in:
\(4.5=\frac{1}{2}(b*2+9.5\frac{db}{dt})\)
We can find \(b\) with:
\(A=\frac{1}{2}bh\rightarrowb=\frac{2A}{h}=\frac{2*92}{9.5}=\frac{184}{9.5}\)
So \(4.5=\frac{1}{2}(2*\frac{184}{9.5}+9.5\frac{db}{dt})\)
\(\rightarrow9=\frac{368}{9.5}+9.5\frac{db}{dt}\)
\(\rightarrow9-\frac{368}{9.5}=9.5\frac{db}{dt}\)
\(\rightarrow\frac{db}{dt}=\frac{9-\frac{368}{9.5}}{9.5}\approx-3.130\)
So the base is decreasing at a rate of 3.130 cm/minute.
