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A square sheet is formed by joining n identical square sheets of same size. If the length of the diagonal of the bigger square sheet so formed is m, then what is the side length of a smaller square sheet?

A square sheet is formed by joining n identical square sheets of same size. If the length of the diagonal of the bigger square sheet so formed is m, then what is the side length of a smaller square sheet? Correct Answer <span class="math-tex">\(\frac{{\rm{m}}}{{\sqrt {{\rm{2n}}} }}\)</span>

Formula used:

Area of square = (side)2

Diagonal = √2 × (side)

Calculation:

Let a nad A  be the side of n identical square and large square.

Diagonal of square = A√2 

⇒ A√2 = m      (given)

⇒ A = m/√2         

Area of large square = sum of the area of small square

⇒ A2 = n × a2

⇒ m2/2 = n × a2     

⇒ a = m/√(2n)

∴ The side of the smaller square sheet is m/√(2n).

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