# the altitude of a triangle is increasing at a rate of 2.500 centimeters/ minute while the area of a triangle is increasing at a rate of 3.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.000 centimeters and the area is 90.000 square centimeters?

The area of a triangle is given by `A = (1/2)*b*h` where b is the base and h is the altitude.

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

The altitude of the triangle is increasing at a rate of 2.5 centimeters/ minute while the area of a triangle is increasing at a...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

The area of a triangle is given by `A = (1/2)*b*h` where b is the base and h is the altitude.

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

The altitude of the triangle is increasing at a rate of 2.5 centimeters/ minute while the area of a triangle is increasing at a rate of 3.0 square centimeters/minute.

When the altitude is 10.0 centimeters and the area is 90.0 square centimeters, the base is 18. This gives:

`3 = (1/2)*18*2.5 + (1/2)*10*((db)/dt)`

=> `(db)/dt = -3.9`

The length of the base of the triangle is decreasing at the rate 3.9 cm/minute

Approved by eNotes Editorial Team