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.
<u>Option A</u>: 10 cm, 6 cm, 8 cm
Using the Pythagorean theorem, we have,
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.
<u>Option B</u>: 14 m, 20 m, 25 m
Using the Pythagorean theorem, we have,
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.
<u>Option C</u>: 7 cm, 8 cm, 10 cm
Using the Pythagorean theorem, we have,
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.
<u>Option D</u>: 3 ft, 6 ft, 5 ft
Using the Pythagorean theorem, we have,
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.