Question 5

A square is constructed on a graph paper which has a square grid of $$1\text{ cm}$$ width. Ram paints all the squares which cross the two diagonals of the square and finds that there are $$19$$ of them. Then the side of the square is

Solution

For a square of side $$n$$ grid units, the two diagonals pass through a total of $$2n-1$$ grid squares in the intended counting of the problem. Thus $$2n-1=19$$, giving $$n=10$$. Since each grid unit is $$1\text{ cm}$$, the side is $$10\text{ cm}$$.

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A square is constructed on a graph paper which has a square grid of $$1\text{ cm}$$ width. Ram paints all the squares which cross the two diagonals of the square and finds that there are $$19$$ of them. Then the side of the square is

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