Answer:
[tex]4\sqrt{21}[/tex]
Step-by-step explanation:
Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
Which in this case:
'c' is hypotenuse. (hypotenuse = 20)
'a' and 'b' are the other sides. (a = x, b = 8)
- [tex]a^{2} +b^{2}= c^{2}[/tex]
- [tex]x^{2} +8^{2} =20^{2}[/tex]
- [tex]x^{2} + 64 = 400[/tex]
- [tex]x^{2} = 336[/tex]
Now we should just take square root from the both sides.
and the answer will be [tex]\sqrt{336}[/tex] or [tex]-\sqrt{336}[/tex], but a side of a triangle can not be a negative number! so the answer will be [tex]\sqrt{336}[/tex].
As you see [tex]\sqrt{336}[/tex] is not the simplest radical.
We can write [tex]\sqrt{336}[/tex] as [tex]\sqrt{16 * 21}[/tex].
And from the laws of radical we can write [tex]\sqrt{16*21}[/tex] as [tex]\sqrt{16} * \sqrt{21}[/tex].
[tex]\sqrt{16} * \sqrt{21} = \sqrt{16}\sqrt{21} = 4\sqrt{21}[/tex]
I hope it helps you. Please choose my answer as the brainliest.
