find the side and perimeter of a square whose diagonal is 10 cm
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Step-by-step explanation:
Let □ ◻ABCD be the given square. l(diagonal AC) = 10 cm Let the side of the square be ‘x’ cm.
In ∆ABC, ∠B = 90° [Angle of a square]
∴ AC2 = AB2 + BC2 [Pythagoras theorem]
∴ 102 = x2 + x2
∴ 100 = 2x2
∴ x2 = 100/2
∴x2 = 50
∴ x = √ 50 50 [Taking square root of both sides]
= √ 25 × 2 25×2 = 5 √ 2 52
∴side of square is 5 √ 2 52 cm. = 4 x 5 √ 2 52
∴ Perimeter of square = 20 √ 2 2 cm
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