Answer: [tex]c=4\sqrt{2}[/tex]
Step-by-step explanation:
For this exercise you need to apply the Pythagorean Theorem. This is:
[tex]h^2=l^2+m^2[/tex]
Where "h" is the hypotenuse of the Right triangle and "l" and "m" are the legs.
In this case, you can identify that:
[tex]h=c\\\\l=a=4\\\\m=b=4[/tex]
Knowing these values, you can substitute them into [tex]h^2=l^2+m^2[/tex]:
[tex]c^2=4^2+4^2[/tex]
Now you must solve for "c":
[tex]c=\sqrt{4^2+4^2}[/tex]
Evaluating, you get:
[tex]c=\sqrt{16+16}\\\\c=\sqrt{32}[/tex]
To simplify the result:
- Descompose 32 into its prime factors:
[tex]32=2*2*2*2*2=2^5[/tex]
- By the Product of powers property, you know that:
[tex]2^5=2^4*2[/tex]
- Make the substitution:
[tex]c=\sqrt{2^4*2}[/tex]
- Finally, knowing that [tex]\sqrt[n]{a^n}=a[/tex], you get:
[tex]c=2^2\sqrt{2}\\\\c=4\sqrt{2}[/tex]
