Math calculus

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The altitude of a triangle is increasing at a rate of 1000 centimeters/minute while the area of the triangle is increasing at a rate of 1500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7000 centimeters and the area is 89000 square centimeters?


I have tried to answer this in so many ways but couldn't get right answer ... Help please !

  • Math calculus -

    Let the base be x cm and the height be y cm

    Area = (1/2)xy cm^2

    dArea/dt = (1/2)(x dy/dt + y dx/dt) ------- #1

    given: dy/dt = 1000 cm/min
    dArea/dt = 1500 cm^2/min

    find dx/dt when y = 7000 cm and Area = 89000 cm^2

    ...........

    when y = 7000 and area = 89000
    (1/2)(x)(7000) = 89000
    x = 178/7

    which leaves dx/dt as the only missing part of #1

    1500 = (1/2)( (178/7)(1000) + 7000(dx/dt) )
    3000 = 178000/7 + 7000 dx/dt
    dx/dt = -157000/49000 cm/min
    = - 157/49 cm/min
    = appr -3.2 cm/min

    At that instant, the base is decreasing at a rate of appr 3.2 cm/min

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