Question

Need help on geometry

Answer 1

`2\sqrt {10}`

Explanation:

Given:

`x=3\sqrt 5`

`y=\sqrt 5`

As seen from the triangle, the triangle is a right angled triangle. Two sides of the triangle are given and we are asked to find the third side.

'x' is the hypotenuse as this side is opposite side to the right angled.

'y' and 'z' are the two legs of the triangle.

Now, using pythagoras theorem,

`x^2=y^2+z^2\\\\(3\sqrt 5)^2=(\sqrt 5)^2+z^2\\\\9* 5=5+z^2\\\\45-5=z^2\\\\40=z^2\\\\z=\sqrt {40}\\\\z=2\sqrt {10}`

Therefore, the measure of the side 'z' is
`2\sqrt {10}`.

Hence, the third option is correct.