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.