Question

2. Find the perimeter of a square if its diagonal is 20v2 cm.
(A) 80 cm
(B) 160 cm (C) 40v2 cm
(D) 20 cm​

Answer 1

$\bigstar$ Question:

$\longrightarrow$ Find the perimeter of a square if its diagonal is 20√2 cm.

$\bigstar$ To Find:

$\longrightarrow$ Perimeter of a square = ?

$\bigstar$ Given:

$\longrightarrow$ Diagonal = 20√2 cm

$\bigstar$ Solution:

It is given that,ABCD is a square.

Picture is attached

$\therefore$ AB = BC = CD = DA = c

According to pythagoras theorem, in ABCD

$AB^2 + AD^2 = BD^2$

$\implies x^2 + x^2 = (20√2)^2$

$\implies 2x^2 = 800$

$\implies x^2 = \frac{800}{2}$

$\implies x^2 =$400

$\implies x = √400$

$\implies x =$20cm

Thus,The Side of the square is 20cm.

Perimeter of square = 4 × Side

Perimeter of square = 4 × 20

Perimeter of square = 80cm

Hence,The perimeter of square is 80cm, Option(A) is correct.

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