Answer:
Option C is correct
value of c is, [tex] 3\sqrt{34}[/tex] units
Step-by-step explanation:
Using Pythagoras theorem;
[tex]\text{Hypotenuse side}^2 = \text{Shorter side}^2+ \text{Longer side}^2[/tex] ....[1]
As per the statement:
A right triangle XYZ, with Z being the right angle and
XZ=15, YZ=9, and XY=c.
Using Pythagoras theorem in triangle XYZ :
Hypotenuse side = XY = c unit
Shorter side = YZ = 9 units
Longer side = XZ = 15 units
Substitute these in [1] we have;
[tex]c^2 = 15^2+9^2[/tex]
⇒[tex]c^2 = 225+81= 306[/tex]
⇒[tex]c = \sqrt{306} =\sqrt{34 \cdot 9} = 3\sqrt{34}[/tex] units
Therefore, the value of c is, [tex] 3\sqrt{34}[/tex] units
