Question

The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?

____ cm/min

Answer 1

dh/dt = 2.5 cm/min, dA/dt = 4 cm^2/min. Area = (1/2)bh, 97 = (1/2)b(8.5). b = 194/8.5.

dA = (1/2)h(db) + (1/2)b(dh).

4 = (1/2)(8.5)db + (1/2)(194/8.5)(2.5), db = (4 - (1/2)(194/8.5)(2.5))/((1/2)(8.5)) =-5.77 cm/min.
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