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Diagonal of a Square is 20 Cm. Find the Length and Perimeter of the Square. - Geometry

Diagonal of a square is 20 cm. Find the length and perimeter of the square.

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Solution

Diagonal of square = 20 cm.
Let side of square = x
∴ x2 + x2 = 202 ..................(By Pythagoras theorem)
∴ 2x2 = 400

∴ x2 = 200
∴ x = `10sqrt2 `cm.
Perimeter of square = 4 × `10sqrt2` =` 40sqrt2`
(i) Side of square =` 10sqrt2` cm.
(ii) Perimeter of square = `40sqrt2` cm.

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