SOLUTION: Among all rectangles that have a perimeter of 102, find the dimensions of the one whose area is largest.
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Question 858158: Among all rectangles that have a perimeter of 102, find the dimensions of the one whose area is largest.
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
If the perimeter = 102, then L + W = 51 (perimeter is 2L + 2W)
The numbers closest together are going to yield the highest area.
Any numbers that equal 51 are going to work. What two numbers are closest to each other? 51/2 = 25.5
Length = 26, Width = 25, Area = 25 * 26 = 650
.
You can test that. Pick any other two. How about 50 and 1?
50 * 1 = 50
Maybe 30 and 21. 30*21=630
20*31=620
5*46 =230
etc, etc, etc. It's always going to be the two numbers closest together that yield the highest area.
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