Question

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

OD=OB=BD/2

OD=L√2/2

Also, By symmetry

DP=CP=CD/2=L/2

Now, In ΔOPD, By Pythagoras theorem

Hypotenuse^2 = Perpendicular^2 + Base^2

⇒ OD^2 = OP^2 + DP^2

(L√2/2) ^2=(2√2) ^2+(l/2) ^2

L^2/4=8

⇒ L^2= 32

⇒ L^2= 4√2 cm

Step-by-step explanation:

I think this is the answer