Question

If diagonal of a square is 13 cm then find its side.

Answer 1

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)`