Find the exact,simplified value of x for this given triangle

Hey there!

Since you are given the two shorter legs of this triangle, 3 and 9, and you are also given that it is a right triangle, you can find x by using the Pythagorean Theorem:
a^2+b^2=c^2

a and b are the two shorter legs and c is the hypotenuse, or x.

Now, plug in your known values:
(3)^2+(9)^2=c^2

Now, simplify and solve for c, or your value of x:
(3)^2+(9)^2=c^2
9+81=c^2
c^2=90
c=[tex] \sqrt{90} [/tex]

Finally, because the answer wants an exact and simplified answer, we must simplify [tex] \sqrt{90} [/tex] to a radical in simplest form by factoring all the square factors from the radicand. In this case, the square factors of [tex] \sqrt{90} [/tex] is [tex] \sqrt{9} [/tex]*[tex] \sqrt{10} [/tex] which would simplify this radical to 3[tex] \sqrt{10} [/tex].

Therefore, your final answer would be x=3[tex] \sqrt{10} [/tex]

Hope this helps and have a nice day!