The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of ....?

Altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm²/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm².

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  • 2 months ago
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    Let "b" and "h" be the base and height of the triangle ABC

    Area of triangle ABC

    A = (1/2) b h

    h = 10 area = 100

    100 = (1/2) x b x 10

    b = (100 x 2)/10

    b = 20

    dA/dt = (1/2) [b (dh/dt) + h (db/dt)]

    h (db/dt) = 2 (dA/dt) - b (dh/dt)

    db/dt = (2/h) (dA/dt) - (b/h) (dh/dt)

    db/dt = (2/10) (2) - (20/10) (1)

    db/dt = (4/10) - (20/10)

    db/dt = -16/10

    db/dt = -1.6 cm/min ( decreasing ) ..................... Answer

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