g The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 160 cm2

Question

Mathematics

Crane

24 February, 03:40

g The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 160 cm2

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Answers (1)

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Greta Oneal · Answer 1

-0.6 cm/min

Step-by-step explanation:

The formula for the area of a triangle is ...

A = (1/2) bh

Solving for the base, we find ...

b = 2A/h

Then the rate of change of the base is ...

b' = 2 (A'h - Ah') / h^2

Filling in the given values, we find the rate of change of the base to be ...

b' = 2 ((2 cm^2/min) (20 cm) - (160 cm^2) (1 cm/min)) / (20 cm) ^2

= 2 (40-160) / 400 cm/min

= - 0.6 cm/min

The base is decreasing at 0.6 cm/minute.