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myrzilka [38]
3 years ago
14

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
Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Answer:

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

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