Question

The length of of diagonal of a sqaure is 50 cm find the perimeter of the sqaure .​

Answer 1

Given

• Length of the diagonal of a square is 50cm.

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To find

• Perimeter of the square.

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Solution

• As we know that each side of the square is equal in length.

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⠀⠀⠀Explanation

• Let ABCD be the required square and each side of the square be x.

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★ Diagonal → AC = 50 cm

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• ABC is a right angled triangle with hypotenuse (AC) = 50cm.

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⠀⠀⠀⠀❍ Using Pythagoras theorem

→ (AC)² = (AB)² + (BC)²

→ (50)² = x² + x²

→ (50)² = 2x²

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Cancelling the square

→ 2x = 50

→ x = 25

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• We get each side of the square i.e., 25cm

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★ Perimeter = 4 × Side

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→ Perimeter = 4 × 25

→ Perimeter = 100 cm

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Hence,

• The perimeter of the square is 100cm.

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