Answer:
{6, 8, 10} is a set which represents the side length of a right triangle.
Step-by-step explanation:
In a right triangle:
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
Now, in the given triplets:
(a) {4, 8, 12}
Here, [tex](4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94[/tex]
So, third side of the triangle 8.94 ≠ 12
Hence, {4, 8, 12} is NOT a triplet.
(b) {6, 8, 10}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10
Hence, {6, 8, 10} is a triplet.
(c) {6, 8, 15}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10 ≠ 15
Hence, {6, 8, 15} is NOT a triplet.
(d) {5, 7, 13}
Here, [tex](5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60[/tex]
So, third side of the triangle 8.60 ≠ 13
Hence, {5, 7, 13} is NOT a triplet.
