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**+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**+5 **

Best Answer

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