Farmer dunphy has 15 metres of fencing .He wants to make a closed rectangular pen.he uses a long wall for one of the sides .Each side of the pen is a whole number in metres .

What is the largest area that the pen can be ?

Draw a diagram!
Space has to be a rectangle.
I am a great fan of diagrams.

You have 15m, but each side must be a whole number of metres.

first work out those possibilities.
eg you can’t have long sides of 5m, that would leave you 5m and the short sides woukd be 2.5m

I tried to make diagram and divide the perimeter such that each side stays in whole numbers still confusing not able to do
Is there any other way to find the area of a pen

If this is a question for
a KS2 child, I would not expect them to use a formula.
The sides need to be whole metres.
That is your starting point.

Aha!
Reading the questions carefully, he has a long wall for one side of it.
So 15 m to make the other 3 sides!
If walk was 5m, he could use 3x5m so area would be 25metres square.
You could work from there?

9m + 2x3m = 27m squared

11m ...and so on.

Definitely one where not reading the question would lead to huge difficulty, as a rectangle with whole number sides can't have an odd perimeter

Being a maths nerd I did of course have to find the formula to maximise the areas allowing non-whole numbers, and if Farmer D could bring himself to use a 7.5m x 3.75m rectangle that would be the biggest possible pen...

As you were