Question 1044224: if breadth of a rectangle is 2/5 of its length and half of the perimeter of a rectangle is 375m. then GCD of length and breadth is ?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Is  supposed to mean Greatest Common Divisor?
If it is so, you would expect the values, in meters, for he breadth and length of the rectangle to be whole numbers, but they turn to be fractions.
THE PROBLEM AS POSTED:
We can define
 = breadth of the rectangle, in meters, and
 = length of the rectangle, in meters,
because that is the same as saying that the breadth of the rectangle is  of its length.
 = half of the perimeter of the rectangle, in meters.
The problem says that  .
So,  .
That is not a whole number. It is a fraction,
so  and  ,
the breadth and length of the rectangle, are not whole numbers.
They are irreducible fractions.
IF THE PROBLEM STATED THAT
the breadth of a rectangle is  of its length and half of the perimeter of a rectangle is 375m,
then bread and length (in meters) can be written as and  ;
 is half of the perimeter of the rectangle, in meters;
 is the equation;
 ,
the breadth is ,
the length is ,
and the GCD of length and breadth is
 , because  and  are coprime, or relatively prime
(they do not have any common factors/divisors other than 1).
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