Question

Find the length of the third side. If necessary, write in simplest radical form. 4 8
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Answer 1

Answer:
`4√(3)`

Explanation:

We can use the pythagorean theorem to solve this.

We will call the length of the unknown side x for now.

Using the theorem, we will get to:

`8^2-4^2=x^2`

`64 - 16 = x^2`

`48 = x^2`

`x = √(48)`

In simplest radical form, it will be:

`4√(3)`

Answer 2

4
`√(3)`

Explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the third side, then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x =
`√(48)` =
`√(16(3))` =
`√(16)` ×
`√(3)` = 4
`√(3)`