(5, 12, 13) are the set of numbers that could represent the length of a right triangle.
Step-by-step explanation:
In any right angle triangle sum of square of the largest side is equal to the sum of square of the other two sides.
Using pythagoras:
![(Hypotenuse)^{2} = Base^{2} + Altitude^{2}](/tpl/images/0326/0093/e4888.png)
where largest side is the hypotenuse.
Case 1: Â ![(10)^{2} \neq (5)^{2} + (5)^{2}](/tpl/images/0326/0093/76476.png)
∵ 100 ≠50
Case 2: Â ![(6)^{2} \neq (4)^{2} + (5)^{2}](/tpl/images/0326/0093/44b4a.png)
36 ≠16 + 25
36 ≠41
Case 3: ![(13)^{2} = (5)^{2} + (12)^{2}](/tpl/images/0326/0093/03694.png)
169 = 25 + 144
169 = 169
Since
, ∴ option C is the correct answer. So, (5, 12, 13) are the set of numbers that could represent the length of a right triangle.
Case 4: Â ![(10)^{2} \neq (7)^{2} + (8)^{2}](/tpl/images/0326/0093/53522.png)
100 ≠49 + 64
100 ≠103