Question

The answer above is NOT correct. The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/ minute while the area of the triangle is increasing at a rate of 5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 7.5 centimeters and the area is 98 square centimeters? The base is changing at cm/min

Answer 1

A = (1/2)bh

98 = (1/2)(7.5)b

98 = 15b, so b = 98/15

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

5 = (1/2)((98/15)(1.5) + (7.5)(db/dt))

5 = (1/2)(980 + 7.5(db/dt))

10 = 980 + 7.5(db/dt)

-970 = 7.5(db/dt)

db/dt = (-129 1/3) cm/min

The base is decreasing at the rate of

129 1/3 cm/min