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# A rectangle has a perimeter of 64 inches and each side has an integer length. How many non-congruent rectangles meet these criteria?

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A rectangle has a perimeter of 64 inches and each side has an integer length. How many non-congruent rectangles meet these criteria?

Guest Mar 29, 2015

#1
+92505
+5

I'll have a go at this one.....!!!

Since the perimeter is 64, the width and the length must be (1/2) of this = 32

And if each is an integer quantity....we have the following possibilites

31 + 1  ... 30+  2 ...  29 + 3....etc.

But notice, when we get to 16 + 16, we can stop....because all combinations after this are just "reversals" of the sums that came before 16 + 16 !!!

So

31 - 16 + 1   = 16  noncongruent rectangles.....!!!!

CPhill  Mar 29, 2015
#1
+92505
+5

I'll have a go at this one.....!!!

Since the perimeter is 64, the width and the length must be (1/2) of this = 32

And if each is an integer quantity....we have the following possibilites

31 + 1  ... 30+  2 ...  29 + 3....etc.

But notice, when we get to 16 + 16, we can stop....because all combinations after this are just "reversals" of the sums that came before 16 + 16 !!!

So

31 - 16 + 1   = 16  noncongruent rectangles.....!!!!

CPhill  Mar 29, 2015