Q. 20 D

# If the length of perpendicular from the intersecting point between two diagonals on any side of square is 2√2 cm, then what is the length of each diagonal of square?

Answer :

Let us consider a square ABCD with diagonals intersecting at ‘O’.

OP is perpendicular to any of its sides such that

OP = 2√2 cm

Let the side of square be ‘L’

Then diagonal of square, BD = L√2

Also,

Diagonals of square bisect each other, therefore

Also, By symmetry

Now, In ΔOPD, By Pythagoras theorem

Hypotenuse^{2} = Perpendicular^{2} + Base^{2}

⇒ OD^{2} = OP^{2} + DP^{2}

⇒ L^{2} = 32

⇒ L^{2} = 4√2 cm

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