Question

What is the length of side s of the square shown below?

Answer 1

C

Explanation:

The diagonal splits the square into 2 right triangles with hypotenuse 6

Using Pythagoras' identity in one of the right triangles.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

s² + s² = 6²

2s² = 36 ( divide both sides by 2 )

s² = 18 ( take the square root of both sides )

s =
`√(18)` =
`√(9(2))` =
`√(9)` ×
`√(2)` = 3
`√(2)` → C

Answer 2

3√2

Explanation:

Pythagoras says s²+s²=6²

so

2s² = 36

s = √18 = √9·2 = √3²·2 = 3√2