Is a triangle with sides of lengths 24, 70 and 74 a right triangle?
1 Answer
Nov 14, 2015
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:
Notice that
#(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