# 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:

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