Is a triangle with sides of lengths 24, 70 and 74 a right triangle?

1 Answer
Nov 14, 2015

Answer:

Yes

Explanation:

#24^2+70^2=576+4900=5476=74^2#

So these side lengths satisfy Pythagoras Theorem.

An alternative way of approaching this might be as follows:

#24#, #70# and #74# are all divisible by #2#, so this triangle is a right angled triangle if and only if a triangle with sides #12#, #35# and #37# is a right angled triangle.

Notice that #35 = 6^2-1#, #37 = 6^2+1# and #12 = 2*6#. This looks like a pattern we could check:

#(a^2-1)^2 = a^4-2a^2+1#

#(a^2+1)^2 = a^4+2a^2+1#

#(2a)^2 = 4a^2#

So:

#(a^2+1)^2 = a^4+2a^2+1 = a^4-2a^2+1+4a^2 = (a^2-1)^2+(2a)^2#

In our case #a=6#, but any number #a# would work.