SOLUTION: You have 16 feet of fence to make a rectangular garden. Each side will measure a whole number of feet. How many different-sized rectangular (exclude squares) gardens can you make?

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Question 1189805: You have 16 feet of fence to make a rectangular garden. Each side will measure a whole number of feet. How many different-sized rectangular (exclude squares) gardens can you make?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

If L and W are the length and the width of a rectangle, then L and W in our problem must be integer numbers satisfying  

    L + W  = 16/2 = 8,   or   L =  8 - W.


and we want to have L > W  (the case L = W = 4 is excluded, by the condition).


So, the possible pairs (dimensions) are


   T  A  B  L  E 
 

     L      W

  ---------------

     7      1

     6      2

     5      3


As you see from the Table, there are three pairs possible dimensions for non-congruent rectangles.

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

L = length
W = width

There are two sides of L and two sides of W
Overall, the perimeter is L+L+W+W = 2L+2W = 2(L+W)

Set this equal to the stated perimeter 16 feet and we can find that
2(L+W) = 16
2(L+W)/2 = 16/2
L+W = 8

The length and width aren't known, but we do know that they add to 8 feet.

If each side of the rectangle is some positive whole number, then here are all the possible combos
LW
71
62
53
We ignore L = 4 and W = 4 because squares are excluded.
The order doesn't matter so something like (L,W) = (7,1) is the same as (L,W) = (1,7).

Each row of that table gives a unique possible rectangle that can be formed based on the conditions stated.

Answer: 3 different rectangles
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