Option A: 10 cm, 6 cm, 8 cm is the set of side lengths form a right triangle.
Explanation:
From the set of side lengths, we need to determine the set that forms a right triangle.
We know that, the hypotenuse of the triangle has the largest measurements.
Thus, from the given set of lengths, let us assume the largest measurement is the hypotenuse.
Option A: 10 cm, 6 cm, 8 cm
Using the Pythagorean theorem, we have,
[tex]10^2=6^2+8^2[/tex]
[tex]100=36+64[/tex]
[tex]100=100[/tex]
Since, both sides of the equation are equal, then the set 10 cm, 6 cm, 8 cm forms a right triangle.
Hence, Option A is the correct answer.
Option B: 14 m, 20 m, 25 m
Using the Pythagorean theorem, we have,
[tex]25^2=14^2+20^2[/tex]
[tex]625=196+400[/tex]
[tex]625\neq 596[/tex]
Since, both sides of the equation are not equal, then the set 14 m, 20 m, 25 m does not forms a right triangle.
Hence, Option B is not the correct answer.
Option C: 7 cm, 8 cm, 10 cm
Using the Pythagorean theorem, we have,
[tex]10^2=7^2+8^2[/tex]
[tex]100=49+64[/tex]
[tex]100\neq 113[/tex]
Since, both sides of the equation are not equal, then the set 7 cm, 8 cm, 10 cm does not forms a right triangle.
Hence, Option C is not the correct answer.
Option D: 3 ft, 6 ft, 5 ft
Using the Pythagorean theorem, we have,
[tex]6^2=3^2+5^2[/tex]
[tex]36=9+25[/tex]
[tex]36\neq 34[/tex]
Since, both sides of the equation are not equal, then the set 3 ft, 6 ft, 5 ft does not forms a right triangle.
Hence, Option D is not the correct answer.
