Question

What is the length of the diagonal of a square of side 8cm, after getting your answer, put it in one decimal place. 13.1cm 12cm 11.4cm 11.3cm

Answer 1

11.3 cm

Explanation:

The diagonal d divides the square into 2 right triangles with legs 8 and hypotenuse the diagonal d.

Using Pythagoras' identity in one of the right triangles, then

d² = 8² + 8² = 64 + 64 = 128 ( take square root of both sides )

d =
`√(128)` ≈ 11.3 cm

Answer 2

`\huge\boxed{c = 11.3 cm}`

Explanation:

Using Pythagorean Theorem:

`c^2 = a^2 + b^2`

Where c is the length of diagonal and a and b are the sides of the square

[Remember that all sides of the square are equal]

=>
`c^2 = 8^2 + 8^2`

=>
`c^2 = 64+64\\`

=>
`c^2 = 128`

Taking sqrt on both sides

=> c = 11.3 cm