## The altitude (i.e., height) of a triangle is increasing at a rate of 2.5 cm/minute while the area of the triangle is increasing at a rate of

Question

The altitude (i.e., height) of a triangle is increasing at a rate of 2.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 84 square centimeters?

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1 week 2021-10-09T20:28:56+00:00 1 Answer 0

The base is decreasing at a rate of 7.8571 centimeters per minute.

Step-by-step explanation:

We are given the following information in the question:

The height of a triangle is increasing at a rate of 2.5 cm/minute The area of the triangle is increasing at a rate of 2.5 square cm/minute. Area of triangle is given by: where A is the area of triangle, b is the base of triangle and h is the height of the triangle.

Differentiating, we get, We have to find rate of change of base of the triangle when the altitude is 7 centimeters and the area is 84 square centimeters

h = 7 cm

A  = 84 square centimeters Putting the values, we get: Thus, the base is decreasing at a rate of 7.8571 centimeters per minute.