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Question
Find the side and perimeter of a square whose diagonal is 10 cm.
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Solution
Let ABCD be the given square.
AC = 10 cm
Let the side of the square be x cm.
∴ AB = BC = x cm
In Δ ABC,
∠ABC = 90° ...(Angle of a square)
∴ by Pythagoras theorem,
AC2 = AB2 + BC2
∴ 102 = x2 + x2
∴ 100 = 2x2
∴ x2 = `100/2`
∴ x2 = 50
∴ x = `5sqrt2`
∴ AB = `5sqrt2` cm
∴ side of a square is `5sqrt2` cm.
Perimeter of a square = 4 × side
= 4 × `5sqrt2`
= `20sqrt2` cm
∴ Side of a square is `5sqrt2` cm and its perimeter is `20sqrt2` cm.
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