The length of a rectangle is increasing at a rate of 3 cms a

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 7 cm and width is 5 cm, how fast is the area of the rectangle increasing? cm^2/s

Solution

Sol:

if length=7cm

width =5cm

Area of rectangle length*width=7*5=35 cm²

^{If length increased by 3 cm/s then}

new length=7+3=10 cm

and if width increases by 7 cm/s

new width=7+5=12 cm

new area of rectangle=10*12=120 cm²

% increase=increase/original*100

=(120-35)/35*100

=85/35*100

=242.857%