On a square gameboard that is divided into n rows of n squares each, k of these squares lie along the boundary of the gameboard. If k is one of the four numbers 10, 25, 34, or 52, what is a possible value for n?
To find a possible value for n, we can consider the number of squares along the boundary of the gameboard.
In a square gameboard divided into n rows of n squares each, we have four sides, and each side has n squares. So, the total number of squares along the boundary is given by 4n.
We are given that the number of squares along the boundary, k, can be either 10, 25, 34, or 52.
We can set up the equation:
4n = k
Substituting the given values for k, we have the following equations:
4n = 10
4n = 25
4n = 34
4n = 52
Solving each equation individually, we find the following possible values for n:
For 4n = 10, dividing both sides by 4 gives n = 2.5, which is not a whole number. So, this value of k doesn't have a valid value for n.
For 4n = 25, dividing both sides by 4 gives n = 6.25, which is not a whole number. So, this value of k doesn't have a valid value for n.
For 4n = 34, dividing both sides by 4 gives n = 8.5, which is not a whole number. So, this value of k doesn't have a valid value for n.
For 4n = 52, dividing both sides by 4 gives n = 13. So, n = 13 is a possible value for this value of k.
Therefore, a possible value for n is 13 when k equals 52.