Question

The diagonal of a square is 10 square root 2 cm then Find is perimeter

Answer 1

★ Given :-

• Diagonal of square = $\sf{10\:\sqrt{2}}$

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★ To Find :-

• Perimeter of square = ?

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★ Solution :-

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∓ Here, it is given that, Diagonal of square is $\sf{10\:\sqrt{2}}$ . And, we have to find the Perimeter of square .

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• First, we will find side of square ----

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∓ As we know, All the sides of square are equal, and the angle is equal to 90° .

✪︎ Let the sides of square be "x" cm .

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$\therefore \: \sf \pmb{By \: Pythagoras \: Theorem } \\ \\ \dashrightarrow \: \sf{(\:10\:\sqrt{2}\:)\:{}^{2} = {x}^{2} + {x}^{2} } \\ \\ \dashrightarrow \: \sf{100 \times 2 = 2 \: {x}^{2} } \\ \\ \dashrightarrow \: \sf{ {x}^{2} = 100} \\ \\ \dashrightarrow \: \sf{x = \sqrt{100} } \\ \\ \dashrightarrow \: \sf \pmb{x = 10\:cm}$

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• Now, we will find Perimeter -----

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$\bull \: \sf \pmb{Perimeter =4 \times side} \\ \\ \dashrightarrow \: \sf{P = 4 \times 10} \\ \\ \dashrightarrow \: \sf \pmb{P = 40 \: cm}$

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★ Hence :-

• Perimeter of square = 40 cm .

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Hope, It'z Help You .... !!