Answer: The length is 12 mm.
Step-by-step explanation:
-Use the Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex]
-Solve:
[tex]a^{2} + 5^{2} = 13^{2}[/tex]
-Multiply 5 and 13 by the exponents:
[tex]a^2+25=169[/tex]
-Subtract 25 from 169:
[tex]a^2+25=169\\ -25 -25[/tex]
[tex]a^2=144[/tex]
-Then, you square root the 144:
[tex]\sqrt{a^2}=\sqrt{144}[/tex]
[tex]a=12[/tex]
-Result:
[tex]a=12[/tex]
