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Question
If diagonal of a square is 13 cm then find its side.
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Solution
Let `square`ABCD be a square.
AC = 13 cm
Let the length of the square be x cm.
In ∆ABC,
∠ABC = 90° ...(angle of square)
From Pythagoras theorem,
AC2 = AB2 + BC2
132 = x2 + x2
2x2 = 169
x2 = `169/2`
x = `sqrt(169/2)`
x = `13/sqrt(2)`
x = `13/sqrt(2)xxsqrt(2)/sqrt(2)`
x = `(13sqrt(2))/2`
x = `6.5sqrt(2)`
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