The altitude of a triangle is increasing at a rate of 2500 centimeters/minute while the area of the triangle is increasing at a rate of 4500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9000 centimeters and the area is 87000 square centimeters?

Question

Note: The "altitude" is the "height" of the triangle in the formula "Area=(1/2)*base*height". Draw yourself a general "representative" triangle and label the base one variable and the altitude (height) another variable. Note that to solve this problem you don't need to know how big nor what shape the triangle really is.

Answer 1

A=(1/2)*b*h, and if h=9000 and A=87000 then b=19.(3)
A'=(1/2)*b'*h+(1/2)*b*h'
2*A'-b*h'=b'*h
2*4500-19.(3)*2500=b'*9000
b'=?

Answer 2

This definitely helped me find the answer to my question. However, why do we add a "2" to A'?

Thank you!