Question

There are 5640 soldiers in an army camp .for the drill session,

the commander wants arrange them in such a way that the number of soldiers in a row is same as the number in any column.can the commander complete his arrangement by using all of them ? Justify your statement. If not ,how many soldiers should be arranged in a row how many will be left out

Answer 1

The Number of soldiers in row = Number of soldiers in row.

Let The Number of soldiers in row = x.

Then Number of soldiers in column = x.

Totally x² soldiers can be arranged.

We can have 75 as x because 75^2 < 5640

So, If arranged in squares, the number of soldiers left over are 5640-75^2 =5640-5625=15.

Each row must contain 75 soldiers