Hello there!
Here, we want to use the Pythagorean Theorem: [tex]a^{2} + b^{2} = c^{2}[/tex].
For problem number 7, we plug 6 and 8 in for a and b. Like this:
[tex]6^{2} + 8^{2} = c^{2}[/tex]
Now we solve. [tex]6^{2}[/tex] is 36. [tex]8^{2}[/tex] is 64.
64 + 36 = 100
Then, we take the square root of 100 to get c.
[tex]\sqrt{100} = 10[/tex]
(There's something special about this triangle. If you want I'll tell you about it in the comments.)
For problem number 8, we do the same exact thing.
[tex]4^{2} + 12^{2} = c^{2}[/tex]
[tex]4^{2} = 16[/tex] and [tex]12^{2} = 144[/tex]
[tex]144 + 16 = 160[/tex]
[tex]\sqrt{160} = 8\sqrt{10}[/tex]
I hope this helps!!
