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  • 5 years ago

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square feet per second, at which the area is changing when AC = 3 is?

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  1. anonymous
    • 5 years ago
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    The hypotenuse AB is 5 and the length of one leg AC is x, then by the Pythagorean Theorem, the length of the other leg BC is sqrt(25 - x^2). So the area of the triangle is A = (1/2)x sqrt(25 - x^2) dA/dt = {(25-2x^2)/[2 sqrt(25-x^2)]} dx/dt Since dx/dt = -2, it follows that when x = 3, dA/dt = {(25 - 18)/[2 sqrt(25-9)]} (-3) = -(-21)/8

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