Question

if the length of the perpendicular on any side of a square from the point if Intersection of the diagonals is 2√2 cm,then what is the length of each diagonal of the square?​

Answer 1

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

Hypotenuse2 = Perpendicular2 + Base2

⇒ OD2 = OP2 + DP2

⇒ L2 = 32

⇒ L2 = 4√2 cm