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 3.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 86 square centimeters? The base is changing at cm/min.

-1.88cm/min

Step-by-step explanation:

Given

dh/dt = 1.5cm/min

dA/dt = 3.5cm²/min

Height h = 10cm

Area A = 86cm²

Required

db/dt

b is the base

h is the height.

Area of a triangle A = 1/2bh

dA/dt = dA/db•db/dt + dA/dh •dh/dt

dA/db = h/2 = 10/2 = 5cm

Get the base

86 = 1/2(10)b

5b = 86

b = 17.2cm

dA/ dh = 1/2b = 1/2(17.2)

dA/dh = 8.6cm

.substitute given values into the formula above;

dA/dt = dA/db•db/dt + dA/dh •dh/dt

3.5 = 5 db/dt + 8.6(1.5)

3.5 = 5 db/dt + 12.9

5 db/dt = 3.5-12.9

5 db/dt = -9.4

db/dt = -9.4/5

db/dt = -1.88cm/min

Hence the base is changing at -1.88cm/min

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