Q-1 How would i solve this with an equation?

Question

The length of a rectangle is increasing at a rate of

5 meters per day and the width is increasing at a rate

of 3 meters per day.

When the length is 9 meters and the width is 21 meters,

then how fast is the AREA changing?

The rate of change of AREA is  square meters per day.

(Enter your answer as an integer.)

Answer 1

L'=5 m/day

w'=3 m/day

L=9 meters

w=21 meters

A=Lw=9(21) =189 m^2

A=Lw

A'= dA/dt= Lw' +wL'

A' =9(3) +21(5)= 27+105

A'= 132 m^2/day = rate of change of Area

in one day L increases from 9 to14, w increases from 21 to 24

after one day A = 14(24) = 336

A increases from 189 to 336, an increase of 336-189=147 m^2 in one day

one day prior L was 9-5=4 and w was 21-3 = 18

one day prior A was 189-4(18) = 189-72 = 117

in one day A increased 117

147+117 = 264, half 264 = 132 m^2/day = rate of change of Area