Answer:
[tex]3 \sqrt{13} [/tex]
Step-by-step explanation:
Use altitude mean Theorem.
"If a triangle altitude splits it up into two right triangles and we are given the side left and right of the altitude then we can use the formula,
[tex] {a}^{2} = lr[/tex]
where a is the altitude, l is the left side of the altitude and r is the right side of the altitude.
We are trying to find the value of a, and we know the lr is
4*9=36
[tex] {a}^{2} = 36[/tex]
[tex]a = 6[/tex]
So we know the altitude is 6.
Know since the right triangle form a right triangle, apply Pythagoren Theorem
[tex] {6}^{2} + {9}^{2} = {r}^{2} [/tex]
[tex]36 + 81 = {r}^{2} [/tex]
[tex]117 = {r}^{2} [/tex]
[tex] \sqrt{117} = r[/tex]
[tex] \sqrt{9} \times \sqrt{13} = r[/tex]
[tex]3 \sqrt{13} = r[/tex]