Answer: Assuming the missing side, c, is the hypotenuse
by the Pythagorean Theorem
c2=a2+b2
=52+122
=169
→c=13
If the missing side, c, is not the hypotenuse
then b, the longer side must be the hypotenuse, and
by the Pythagorean Theorem
b2=c2+a2
or
c2=b2−a2
=122−52
=119
→c=√119
Answer link
George C.
May 24, 2015
Use Pythagoras theorem: "The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides"
a2+b2=52+122=25+144=169=132
So the hypotenuse of your triangle has length 13.
You have probably encountered the 3-4-5 triangle. The 5-12-13 triangle is part of the same sequence of right angled triangles with integer length sides:
If k is a non-negative integer, then
a=2k+3
b=a2−12=2k2+6k+4
c=a2+12=2k2+6k+5
are the lengths of the sides of a right angled triangle.
