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Question 770026: the sum of length and width of a rectangle is an odd number. what can be the perimeter of the rectangle ?
can you please give me the solution .. i really need your help thank you.
Found 2 solutions by josgarithmetic, ramkikk66:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! One of the distances must be odd and the other distance must be even.
Let m and n be natural numbers.
Distances of the sides of the rectangle are 2m and 2n+1. We have no restriction on the order between m and n.
The sum of the distances of each direction on this rectangle (the length plus width) is 2m+2n+1=2(m+n)+1;This sum is an odd number.
The perimeter will be 2*(2(m+n)+1)=4(m+n)+2, which is even.
No further result on the sum is possible without having more information.
Answer by ramkikk66(644) (Show Source):
You can put this solution on YOUR website!
the sum of length and width of a rectangle is an odd number. what can be the perimeter of the rectangle ?
Ans:
Remember that:
Sum of 2 even numbers is always even
Sum of 2 odd numbers is also always even
Sum of an odd and even number is always odd
So, since the sum of L + W is odd, it is clear that one of them is odd and the
other is even.
Now, perimeter is given by 2*(L+W) and since it is a multiple of 2, the perimeter
is always even. In fact, perimeter of any rectangle is always even.
That is all you can conclude about the perimeter, given the information.
Additionally, the area of the rectangle - since it is the product of an odd and
even number, will also be even.
:)
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