Question

Find side and perimeter of a square whose diagonal is 10 cm

Answer 1

Step-by-step explanation:

In a square of side say a cm, any diagonal divide the square into two right triangles of equal dimensions.

Thus a² + a² = 102

⇒ 2a² = 100

⇒ a² = 50

a = 5 √2 cm

perimeter = 4a

= 4×5 √2

= 20 √2

Perimeter of square = 20 √2cm

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hope it helps u......

Answer 2

$Let \: side \: of \:a \: square = a \:cm$

$i ) Diagonal \:of \:the \:square (d) = 10 \:cm$

$\implies \sqrt{2} a = 10$

/* Multiplying both sides by √2, we get */

$\implies \sqrt{2} \times \sqrt{2} a = 10\times \sqrt{2}$

$\implies 2 a = 10\times \sqrt{2}$

/* Dividing bothsides by 2 , we get */

$\implies a = 5\sqrt{2}\:---(1)$

$ii ) Perimeter \:of \:the \:square = 4a \\= 4 \times 5\sqrt{2} \\= 20\sqrt{2} \:cm$

Therefore.,

$\red { Side \:of \:the \:square } \green {= 5\sqrt{2}\:cm}$

$\red { Perimeter \:of \:the \:square } \green {= 20\sqrt{2}\:cm}$

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