Can someone lend a hand with this? Thanks...
I want to plant a garden 10 yards long and 10 yards wide. So I bought 40 yards (10 + 10 + 10 + 10 ) of fencing for the perimeter of the my garden. My wife said I need to go more along one direction and smaller on the other (Long and narrower – increase the length and reduce the width, rather than both being 10), still keeping the perimeter same to use all the wire I had brought. For example, she said go 15 yards on the length and only 5 yards wide (Total perimeter is still 15 + 5 + 15 +5 i.e. 40 yard of wire).
However, with these measurements my garden will be only 15 * 5 or 75 square yards, 25 square yards smaller. My wife doesn’t believe me.
I want to use algebra to prove it to her that the best shape (the largest garden) I can get, still using all the wire I have (i.e. keeping the perimeter same), is the square garden, 10 * 10 .