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 combosWe 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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