related rates: if square's diag. increases at 3 in/min, find

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ba91c

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Working on related rates, I am struggling with the problem-- I f a diagonal of a square increases at a rate 3 inches per minute, when the area of the square is 18 square inches how fast is the perimeter increasing?

A=s[sup:2zphepl0]2[/sup:2zphepl0] P=4s dh/dt=3/min
P=4s=4(h[sup:2zphepl0]2[/sup:2zphepl0]/sqrt2)
 
ba91c said:
I f a diagonal of a square increases at a rate 3 inches per minute, when the area of the square is 18 square inches how fast is the perimeter increasing?
Click to expand...
Draw the square. Label the lengths of the sides with some variable.

Draw the diagonal. Note the sort of triangle formed. Write down the formula relating the sides of this triangle.

Use the formula for the area A of a square with side-length s, along with the provided area value, to find the length of the sides at the given point in time.

Differentiate the Theorem (mentioned above) with respect to time t. Note that you are given that one of the variables in this Theorem is given as increasing at 3 in/min. Plug this value in. Also, plug in the value you obtained for the sides' lengths at this point in time. Solve for the rate of change in the lengths of these sides.

Take the formula for the perimeter P of a square with side-length s. Differentiate with respect to the time t. Plug in the value you obtained earlier, and solve for the rate of change in the perimeter.

Apply the correct units to your final answer.

If you get stuck, please reply with a clear listing of your work and reasoning so far. Thank you! :D

Eliz.
 
Re: calculus relating rates

Thank you so much!!!! I got the answer by following your directions. Thanks!!! :D
 
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