Question

Fjnd the side and lerimeter of a square whose diagonal is 10 cm.​

Answer 1

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

$Diagonal (d) = 10 \:cm \: ( Given )$

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

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

$\implies \sqrt{a} = 5$

/* On squaring both sides,we get */

$\implies a = 25 \:cm$

$Perimeter \: of \: the \: square = 4a$

$= 4 \times 25$

$= 100 \:cm$

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Answer 2

Answer:-

• Side = $\bf\dfrac{10}{\sqrt{2}}$ cm.

• Perimeter = $\bf 10\sqrt{2}$ cm.

Explanation:-

Given:-

• Diagonal of a square = 10 cm.

To Find:-

• Side of the square.

• Perimeter of the square.

Formula Used:-

$\\ \bf\longrightarrow D = \sqrt{2}\times S...(1)$

$\\ \bf\longrightarrow P = 4\times S...(2)$

Where,

• D = Diagonal.
• S = Side.
• P = Perimeter.

Now,

Diagonal of the square is given 10cm.

So by using formula (1) we get,

$\\ \tt\mapsto D = \sqrt{2}\times S.$

$\\ \tt\mapsto 10 \: cm = \sqrt{2} \times s.$

$\\ \bf\mapsto \boxed{ \bf s = \dfrac{10}{ \sqrt{2} } \: cm .}$

Therefore the side of the square is $\bf\dfrac{10}{\sqrt{2}}\:\:cm.$

Again,

By using formula (2) we get,

$\\ \tt\mapsto P = 4 \times s.$

$\\ \tt\mapsto P = 4 \times \frac{10}{ \sqrt{2} }\: cm.$

$\\ \tt\mapsto P = \cancel{ \sqrt{2}} \times \sqrt{2} \times \frac{4}{ \cancel{ \sqrt{2}} } \: cm .$

$\\ \bf\mapsto \boxed{ \bf P = 10 \sqrt{2} \: cm.}$

Therefore The Perimeter Of The Rectangle Is $\bf 10\sqrt{2}$ cm.

Therefore,

• Side = $\bf\dfrac{10}{\sqrt{2}}$ cm.

• Perimeter = $\bf 10\sqrt{2}$ cm.