Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2? cm2/s

Step-by-step explanation:

The rate if increase of side of square is 7cm/s

dL/dt=7

At what area is the area increasing

dA/dt=?

Areas of square is give to be 36cm²

Analysis

Let L be the length of each side of the square, a square has equal side.

Area of square is give as L²

Area=L²

L²=36

i.e L=√36

L=6cm

Therefore at t=0 L=6cm and A=36cm²

A=L²

dA/dL=2L

Given that, dL/dt=7

Multiply the two differential together

dA/dt= dA/dL × dL/dt

dA/dt= 2L × 7

dA/dt= 2×6×7

dA/dt= 84cm²/s

The rate of increase of the square is 84cm²/s

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6