Question

Find the side and perimeter of a square whose diagonal is 10 cm.
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Answer 1

We're given a square with diagonal 10 cm.

Let's consider that square as ABCD.

In ΔABD,

According to the Pythagoras theorem,

$\implies \sf \: \: {AB}^{2} + {AD}^{2} = {BD}^{2}$

$\implies \sf \: \: {a}^{2} + {a}^{2} = {10}^{2}$

$\implies \sf \: \: {2a}^{2} = 100$

$\implies \sf \: \: {a}^{2} = \dfrac{100}{2}$

$\implies \sf \: \: {a}^{2} = 50$

$\implies \sf \: \: a = \sqrt{50 }$

$\implies \sf \: \: \boxed{ \green{ \sf{a </p><p>= 5 \sqrt{2} \: cm }}}$

Thus, side of the square is 5√2 cm .

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Now, As we know that,

Perimeter of a square = 4 × side

$\implies \sf \: \: Perimeter = 4 \times a$

$\implies \sf \: \: Perimeter = 4 \times 5 \sqrt{2}$

$\implies \sf \: \: \boxed{ \sf{ \blue{ Perimeter = 20 \sqrt{2} \: cm}}}$

Hence, perimeter of the square is 20√2 cm .

Answer 2

Please refer to the attachment.