SOLUTION: Please assist me on this problem:
A rectangle whose sides are changing in length has a constant area of 100 square meters. Find the length of the rectangle when its width is decre
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Question 1026882: Please assist me on this problem:
A rectangle whose sides are changing in length has a constant area of 100 square meters. Find the length of the rectangle when its width is decreasing at a rate of 1 meter per second and its length is increasing at a rate of 1 meter per second.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
L * W = 100, where L is length and W is width
:
differentiate both sides of = by t which is time
:
L * dW/dt + W * dL/dt = 0
:
(L * (-0.1)) + (100/L * (0.1)) = 0
:
-0.1L + (10/L) = 0
:
-0.1L^2 + 10 = 0
:
L^2/10 = 10
:
L^2 = 100
:
***************
L = 10 meters
***************
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