Question

A square has diagonals of length 24 cm, then the sides of the square in cm​

Answer 1

Answer:

given,

diagonal of square = 24cm

also, diagonal of square=√2*side

or, √2*side=24

=> side =24/√2

=> side = 24√2/2

=>side = 12√2cm

therefor, the side of the square is 12√2cm

Answer 2

Given:

The square's diagonals are 24 cm each

To find:

The length of the sides of the square

So,

In the attached image ABCD is the respective square,

And AC ad BD are two diagonals of the square.

We know that all four interior angles of the square are 90°.

ΔADC,

AD = CD (sides of the square)

∠ADC = 90°

[Using Pythagoras Theorem]

⇒ (AD)² + (DC)² = (AC)²

⇒ (AD)² + (AD)² = (AC)²

[As AD = CD]

⇒ 2(AD)² = (24)²

⇒ 2(AD)² = 576

⇒ (AD)² = 576 ÷ 2

⇒ (AD)² = 288

⇒ AD = 16.97 cm

Hence,

Each side of the square is 16.97 cm