Question

If the sides of a square measure 10 square root 6 units then find the length of the diagonal

Answer 1

20
`√(3)`

Explanation:

The diagonal splits the square into 2 right triangles

Using Pythagoras' identity on one of the right triangles

With legs 10
`√(6)` and hypotenuse the diagonal d, then

d² = (10
`√(6)` )² + (10
`√(6)` )² = 600 + 600 = 1200 ( take square root of both sides )

d =
`√(1200)` =
`√(400(3))` =
`√(400)` ×
`√(3)` = 20
`√(3)`