Asked by Anne
I have 100 feet to surround three sides of a rectangle. What is the largest area that I can enclose?
Answers
Answered by
drwls
50 x 25 = 1250 ft^2.
Try 52 x 24 and 48 x 26 (using the same 100 foot length) and see what you get.
The maximum area can be derived using calculus or algebraically by "completing the square".
If x is the length of two parallel sides, the other side length is 100 -2x and the area is
A = x*(100 - 2x) = 100x - 2x^2
= 1250 - 2(x - 25)^2
Now can you see why A cannot exceed 1250 ?
Try 52 x 24 and 48 x 26 (using the same 100 foot length) and see what you get.
The maximum area can be derived using calculus or algebraically by "completing the square".
If x is the length of two parallel sides, the other side length is 100 -2x and the area is
A = x*(100 - 2x) = 100x - 2x^2
= 1250 - 2(x - 25)^2
Now can you see why A cannot exceed 1250 ?
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