How do you find the missing side of the right triangle with legs: a = 5, b = 12?

2 Answers
May 24, 2015

Assuming the missing side, c, is the hypotenuse
by the Pythagorean Theorem
#c^2 = a^2+b^2#
# = 5^2 +12^2#
# = 169#
#rarr 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
#b^2 = c^2+ a^2#
or
#c^2 = b^2-a^2#
#= 12^2-5^2#
#= 119#
#rarr c = sqrt(119)#

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"

#a^2 + b^2 = 5^2 + 12^2 = 25 + 144 = 169 = 13^2#

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=(a^2-1)/2=2k^2+6k+4#

#c=(a^2+1)/2=2k^2+6k+5#

are the lengths of the sides of a right angled triangle.