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9 February, 09:22

The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 12 square cm/min. at what rate is the base of the triangle changing when the height is 4 centimeters and the area is 12 square centimeters?

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  1. 9 February, 11:04
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    Given Information:

    - Rate of height = 2 cm/min

    - Rate of area = 12 cm^2/min

    - Initial height = 4 cm

    - Initial area = 12 cm^2

    Calculation:

    - Find Initial base using initial height and area:

    Since A = 1/2 * b * h; Therefore, 12 = 1/2 * b * 4

    Solve for b: 12 = 2b; Therefore, b = 6

    - Find rate of base:

    after 1 minute: height increased 2 cm, area increased 12 cm^2

    which is: height = 6, area = 24 < - - (using these, find base)

    24 = 1/2 * b * 6; 24 = 3b; b = 8 (after 1 min)

    Therefore, since base changed from 6 to 8 the rate is 2 cm/min

    Answer: 2 cm/min
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