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?

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.

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363