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The base of a triangle is shrinking at a rate of 5 cm/s and the height of the triangle is increasing at a rate of 9 cm/s. Find the rate at which the area of the triangle changes when the height is 12 cm and the base is 4 cm.

Provide your answer below:
The rate of change of the area of the triangle is ___ cm²/s.

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Answer:

Step-by-step explanation

Area of a triangle

      A = ½bh

dA/dt = ½(b(dh/dt) + h(db/dt)

dA/dt = ½(4(9) + 12(-5))

dA/dt = ½(36 - 60)

dA/dt = ½(-24)

dA/dt = -12 cm²/s

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