Question

Which expression can be used to determine the length of segment ZY?

Answer 1

Option 2:
`YZ = \sqrt{(3)^(2)+(8)^(2) }`

Explanation:

We can see that XYZ is forming right angled triangle in the given figure

where XY is Perpendicular.

XZ is Base.

YZ is Hypotenuse .

Length of XY is 3 units (refer figure)

Length of XZ is 8 units (refer figure)

Now to calculate length of ZY we will use Pythagoras theorem i.e.

`(Hypotenuse)^(2) = (Perpendicular)^(2) +(Base)^(2)`

By applying this theorem :

`(YZ)^(2) = (XY)^(2) +(XZ)^(2)`

`(YZ)^(2) = (3)^(2) +(8)^(2)`

⇒
`YZ = \sqrt{(3)^(2)+(8)^(2) }`

Thus Option 2 is the correct expression to determine length of ZY i.e.
`YZ = \sqrt{(3)^(2)+(8)^(2) }`