SOLUTION: A rectangular garden is enclosed so that the river borders 1 side and 300m of fencing are used for the other 3 sides.
a)What is the formula for the area in terms of x and y?
b)
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Question 286594: A rectangular garden is enclosed so that the river borders 1 side and 300m of fencing are used for the other 3 sides.
a)What is the formula for the area in terms of x and y?
b)What is the formul that relates x and y to the perimeter?
c)Write a formulaa for the area in terms of x only
d)What are the dimensions of the garden if the area is a maximum?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the length of the side bordering the river =
Let the 2 sides perpendicular to the side bordering the river =
given:
a) m2
b) m
----------------
c)
is a maximum halfway between the 2 roots. First I'll find the roots
The roots are and
The midpoint is
d)The dimensions that maximize area are 75 x 150
check:
Just vary the dimensions a little bit, and Area should decrease
m2
Suppose:
-note that
and as it should
It decreased by m
OK
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