SOLUTION: 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

Algebra.Com
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.
:)

RELATED QUESTIONS

convert these repeating decimals. 1. 99.999 42.242424 57.357357357... (answered by fcabanski)
im stumped; can you help? "The perimeter of a rectangle is twice the sum of its length (answered by josmiceli)
Can you please help me on this question: If the width of a rectangle is (x+7) cm and its... (answered by nerdybill,Math_prodigy)
The length of a rectangle is three more than twice the width. The perimeter is 42 inches. (answered by fractalier)
The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width... (answered by tw23279)
The lenght and width of a rectangle can be represented by two consecutive odd integers.if (answered by josgarithmetic)
The length of a rectangle is 10 inches more than the width. the perimeter of the... (answered by mananth)
The length of a rectangle is 6 inches more than width. The perimeter of the rectangle can (answered by ikleyn)
The perimeter of a rectangle is equal to twice the sum of its length and its width. one... (answered by math_helper)