Question

The diagonal of a square is 20 cm. What is the length of the side of this square? Give your answer as an exact surd in its simplest form.

Answer 1

Answer:

side-length is 10√2.

Step-by-step explanation:

Let the length of side of that square be a.

 We know, sides of squares intersect the adjacent side at 90°.

     Using Pythagoras theorem:

⇒  side^2 + side^2 = diagonal^2

⇒ a^2 + a^2 = diagonal^2

⇒ 2a^2 = diagonal^2

⇒ a√2 = diagonal

⇒ a√2 = 20cm    { given, diagonal = 20cm}

⇒ a = (20/√2) cm

⇒ a = ( 20√2 ) / 2   { divide as well as multiply by √2 }

⇒ a = 10√2

⇒ a = 10 * 1.414        { √2 ≈ 1.414 }

⇒ a = 14.14 cm

    or a = 10√2 cm

Answer 2

Answer:-

Let the side of the square be "s" cm.

If we assume that the diagonal divides the square into two triangles Then,

(Hypotenuse)² = (Side)² + (Side)²

(20)² = s² + s²

400 = 2s²

s² = 400/2

s² = 200

s = √200

s = 10√2 cm .

(or)

We know that,

Side of a square = diagonal/√2

s = 20/√2

s = 10√2 cm.

Hence, the side of the square = 10√2 cm.