Question

find perimeter of a square if it's diagonal is 7 root 2 a)28 root 2 cm 2 b)28 cm c) 28 root 8 cm d) 14 cm

Answer 1

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Here is your answer.
Let the side of the Square is x cm
Diagonal is 7√2 cm

Using Pythagoras Theorem
${x}^{2} + {x}^{2} = (7 \sqrt{2} ) {}^{2} \\ \\ 2 {x}^{2} = 49 \times 2 \\ \\ {x}^{2} = \frac{49 \times 2}{2} \\ \\ x = \sqrt{49} \\ \\ x = 7$
Now Side of the Square is 7 cm

As we know the formula
Perimeter of Square is = 4× side
$= 4 \times 7 \\ \\ = 28 \: cm$
Therefore Perimeter of Square is 28 cm

Option (b) 28 cm is correct answer

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Answer 2

Hi friends

Here is your answer.

Let the side of the Square is x cm

Diagonal is 7√2 cm

Using Pythagoras Theorem
${x}^{2} + {x}^{2} = (7 \sqrt{2} ) {}^{2} \\ \\ 2 {x}^{2} = 49 \times 2 \\ \\ {x}^{2} = \frac{49 \times 2}{2} \\ \\ x = \sqrt{49} \\ \\ x = 7$


Now

Perimeter of Square is = 4× side
$= 4 \times 7 \\ \\ = 28 \: cm$

Perimeter of Square is 28 cm