# Rate of change of the area of the rebgion

by fifaking7
Tags: rate, rebgion
 P: 12 1. The problem statement, all variables and given/known data A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing? 2. Relevant equations a=1/2bh 3. The attempt at a solution x^2 + 4^2= 5^2 x=3 da/dt= 1/2b(db/dt)(dh/dt) I think i started it up wrong and I don't know where to go next..
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 Quote by fifaking7 1. The problem statement, all variables and given/known data A board 5 feet long slides down a wall. at the instant the bottom end is 4 feet from the wall, the other end is moving down the wall the rate of 2 feet per second.at that moment how fast is the area of the region between the board, the ground and the wall changing? 2. Relevant equations a=1/2bh 3. The attempt at a solution x^2 + 4^2= 5^2 x=3 da/dt= 1/2b(db/dt)(dh/dt) I think i started it up wrong and I don't know where to go next..
What is the shape of the region below the board and above the ground at the moment under consideration?
 P: 12 just a normal triangle drawn on a line like a typical triangle leaning against a wall problem.
 Emeritus Sci Advisor HW Helper PF Gold P: 7,819 Rate of change of the area of the rebgion Neither end of the board is touching the ground, so it's not a triangle.
P: 296
 Quote by fifaking7 2. Relevant equations a=1/2bh da/dt= 1/2b(db/dt)(dh/dt)
Have another look at that derivative. It looks like the product rule hasn't been applied properly. Also one of those b/h is x. You'll have to stay consistent with your variable names.
 P: 12 that is how it looks
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 Quote by fifaking7 that is how it looks
You're right. I misread the problem.

When you said x=3, that should be h=3 .

In general, how are b and h related, considering that they're legs of a right triangle?
 P: 12 i said b= 4ft and h=3 ft
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 Quote by fifaking7 i said b= 4ft and h=3 ft
That's what b & h are at the instant that h = 4 ft, but how are they related in general?

(Use the Pythagorean theorem.)
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 Quote by fifaking7 i said b= 4ft and h=3 ft
The crucial point that you seem to be missing is that you need to figure out what is happening as the board slides down the wall, so h moves from more than 3 ft to less than 3 ft (and, at the same time, b moves from less than 4 ft to more than 4 ft). When that is happening, the area of the triangle is changing, and that is what you are supposed to be reckoning. So, you need to let b and h be variables, not fixed numbers.

RGV
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