Question

Find the perimeter of a square if its diagonal is `10sqrt2` cm:

विकल्प

• 10 cm

• `40sqrt2` cm 

• 20 cm 

• 40 cm

Answer 1

40 cm

Explanation:

It is given that ABCD is a square.

∴ AB = BC = CD = DA = x (say)

According to Pythagoras theorem, in ∆ABD

AB² + AD² = BD²

⇒ `x^2 + x^2 = (10sqrt2)^2`

⇒ 2x² = 200

⇒ x² = 100

⇒ x = `sqrt100`

x = 10 cm

Hence, the side of the square is 10 cm.

Now, Perimeter of a square = 4 × side

= 4 × x

= 4 × 10

= 40

Hence, the correct option is 40 cm.