Respuesta :
Answer:
The base is reducing at a rate of 3.4cm per min.
Step-by-step explanation:
Let The Height of the Triangle, h
Area of the triangle = A
Area of a Triangle, [tex]A= \frac{1}{2}bh[/tex]
When [tex]A=190 cm^2, h=10cm[/tex]
[tex]190= \frac{1}{2}*b*10\\b=38cm[/tex]
[tex]\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,[/tex]
[tex]2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min[/tex]
The base is reducing at a rate of 3.4cm per min.
