Question

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

Answer 1

`|ZY|=√(8^2+3^2)`

Explanation:

ZY is the hypotenuse of triangle XZY.

The two shorter legs are;

YX=3 units

and

XZ=8 units.

According to the Pythagoras Theorem;

`|ZY|^2=|XZ|^2+|YX|^2`

This implies that;

`|ZY|^2=8^2+3^2`

We take the positive square root to obtain;

`|ZY|=√(8^2+3^2)`

The second choice is correct

Answer 2

`\sqrt{8^(2) + 3^(2) }`

Explanation:

We see that this is a rectangle triangle, and that the ZY side is the hypotenuse.

It's length is then square root of the sum of the squares of the other sides:

`hyp = \sqrt{a^(2) + b^(2) }`

So, in this case:

`ZY = \sqrt{8^(2) + 3^(2) }`

The 8 and 3 numbers are easy to get from the graphic... and the order doesn't matter (8² + 3² = 3² + 8²).

That's an easy rule to remember.

I hope it helps.