Question

Given the length of three sides of a triangle, which is a right triangle?
(1) 10,26,24
(2) 20,12,18
(3) 30,15,26
(4) 40,50,80

Answer 1

A) you can figure this out by testing each with the Pythagorean Theorem

a^2 +  b^2 =c^2 (c is the biggest side)

Answer 2

The aides of a right triangle will always satisfy the Pythagorean relationship ...

                   a² + b²=  c²

We can take each of these and try it out:

(1) ... 10² + 24² = 100 + 576  = 676
         √676 = 26  Yes.

(2) ... 12² + 18²  =  144 + 324  =  468
           √468  =  21.6, not 20.  No.

(3) ... 15² + 26²  =  225 + 676  =  901
         √901  =  30.017  Awfully close.  As an engineer, I'll buy this one. Yes.

(4) ...  40² + 50²  =  1,600 + 2,500  =  4,100
          √4,100  =  64.03, not 80.  No.