Question

He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?

Answer 1

By definition, the area of a triangle is given by:
A = (1/2) * (b) * (h)
Where,
b: base of the triangle
h: height of the triangle
Deriving the area we have:
A '= (1/2) * ((b') * (h) + (b) * (h '))
Clearing b' we have:
b '= (2A' - (b) * (h ')) / (h)
We must look for the value of the base:
A = (1/2) * (b) * (h)
Substituting values:
89000 = (1/2) * (b) * (10000)
b = (89000) / (5000)
b = 17.8 cm
Then, the speed at which the base changes is:
b '= (2 * (3500) - (17.8) * (3000)) / (10000)
b '= -4.64 cm / min
Answer:
The base of the triangle is decreasing at:
4.64 cm / min