Q20 of 99 Page 264

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?

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


Hypotenuse2 = Perpendicular2 + Base2


⇒ OD2 = OP2 + DP2






⇒ L2 = 32


⇒ L2 = 4√2 cm


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