Question

In the length of perpendicular from the intersecting point between two diagonals on
any side of square is 2V2cm, then what is the length of each diagonal of square?​

Answer 1

Answer:

root32

Step-by-step explanation:

Answer 2

Answer:

8cm

Step-by-step explanation:

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

⇒ (L√2/2)² = (2√2)² + (L/2)²

⇒ L²/2 = 8 + L²/4

⇒ L²/2 - L²/4 = 8

⇒L²/4 = 8

⇒ L² = 32

⇒ L = √32

THEREFORE DIAGONAL AC = √32 × √2

= √32×2

= √64

= 8cm

ANS:- 8cm

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