find the diagonal of a square whose each side is x
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By Pythagoras theorem,
Diagonal = √x² + x²
Diagonal = √2x²
Diagonal = √2 x
Answer: √2 × x
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As you can see, a diagonal of a square divides it into two right triangles, BCD and DAB. The diagonal of the square is the hypotenuse of these triangles. We can use Pythagoras' Theorem to find the length of the diagonal if we know the side length of the square.
As a formula:
diagonal = √ s 2 + s 2
where s is the length of any side
which simplifies to:
s √ 2
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