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20 May, 04:17

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

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  1. 20 May, 07:33
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    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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