Answer:
=6√3 the third option.
Explanation:
We can use the Pythagoras theorem to find the value of y. We need two equations that include y.
a²+b²=c²
c=9+3=12
x²+y²=12²
x²=144 - y².........i (This is the first equation)
We can also express it in another way but let us find the perpendicular dropped to c.
perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.
y²=(x²-9)+9²
y²=x²+72
x²=y²-72....ii( this is the second equation
Let us equate the two.
y²-72=144-y²
2y²=144+72
2y²=216
y²=108
y=√108
In Surd form √108=√(36×3)=6√3
y=6√3