Question

abcd is a square of side 6 cm find the length of the diagonal​

Answer 1

Length of the diagonal = 6√2 cm

Given

ABCD is a square of side 6 cm

To Find

Length of the diagonal , AC or BD

Solution

Given ,

AB = 6 cm

BC = 6 cm

AD = ? cm

Apply Pythagoras theorem  ΔABC ,

⇒ AB² + BC² = AD²

⇒ 6² + 6² = AD²

⇒ AD² = 72

⇒ AD = 6√2 cm

So , Length of the diagonal = 6√2 cm

In the same way , we can apply Pythagoras theorem for ΔBAD too for finding diagonal .

Answer 2

Given ,

The side of square is 6 cm

By pythagoras theorem ,

$\tt \mapsto {(H)}^{2} = {(6)}^{2} + {(6)}^{2}$

$\tt \mapsto {(H)}^{2} = 36 + 36$

$\tt \mapsto {(H)}^{2} = 72$

$\tt \mapsto H = \sqrt{72}$

$\tt \mapsto H = 6 \sqrt{2} \: \: cm$

Therefore , the length of diagonal of square is 6√2 cm