Maximum area of rectangle with given perimeter.

Feb 2009
59
0
Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

any help would be great!
 

mr fantastic

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Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

any help would be great!
A = xy.

100 = 2x + 2y => y = 50 - x.

Therefore A = x(50 - x). This is a parabola. Find the A-coordinate of its maximum turning point.
 
May 2010
78
6
Tanzania
Area = \(\displaystyle -X^2 + 50x\)

Solve for vertex using line of symmetry equation \(\displaystyle x = - b/2a\)

\(\displaystyle x = -50/-2 , x = 25 \)
Hence, find y by substituting back into \(\displaystyle y = -2x+50 \)