Question

A square has diagonals of length 10 cm. Find the sides of the square

Answer 1

5
`√(2)`

Explanation:

The diagonal divides the square into 2 right triangles.

let s be the side of the square with the diagonal being the hypotenuse.

Applying Pythagoras' identity to one right triangle, gives

s² + s² = 10² , that is

2s² = 100 ( divide both sides by 2 )

s² = 50 ( take the square root of both sides )

s =
`√(50)` =
`√(25(2))` =
`√(25)` ×
`√(2)` = 5
`√(2)`