Question

The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 88 square centimeters?

Answer 1

why don't you try this one now.

Answer 2

i solved like 5 of these.

Answer 3

Ok, I'll try it and post the answer that I get and you let me know if I got it right.

Answer 4

ok

Answer 5

-.76?

Answer 6

huh? It can't be negative, the area is increasing.

Answer 7

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

Answer 8

dA/dt = 5
dh/dt = 1
h=10
A=88
db/dt - ?

Answer 9

10 = b*1 + 10*db/dt

Answer 10

10 = b + 10(db/dt)

Answer 11

Now all we gotta do is figure out b when A = 88 and h = 10
A = (1/2)b*h
88 = (1/2)b*10
88 = 5b
b = 88/5

Answer 12

10 = b + 10(db/dt)
10 = 88/5 + 10(db/dt)
50 = 88 + 50(db/dt)
50-88 = 50(db/dt)
-38 = 50(db/dt)
db/dt = -0.76. You were right!

Answer 13

hmm I guess the height is increasing pretty fast, so that the area manages to increase while the base decreases.

Answer 14

Good job!

Answer 15

Yay! Thanks!!!