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 3500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7000 centimeters and the area is 87000 square centimeters?

Question

x=???

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

so, did you draw a diagram as suggested?

a = 1/2 bh
so, b = 2a/h
da/dt = 1/2 (db/dt * h + b * dh/dt)
Now just plug in your values:
3500 = 1/2 (db/dt * 7000 + 2*87/7 * 2500)
db/dt = -7.88