Question

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

Answer 1

Answer:

$\sqrt{8^{2} + 3^{2} }$

Step-by-step 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.

Answer 2

Answer:

$|ZY|=\sqrt{8^2+3^2}$

Step-by-step 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;

$|ZY|=\sqrt{8^2+3^2}$

The second choice is correct