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,
![10^2=6^2+8^2](https://tex.z-dn.net/?f=10%5E2%3D6%5E2%2B8%5E2)
![100=36+64](https://tex.z-dn.net/?f=100%3D36%2B64)
![100=100](https://tex.z-dn.net/?f=100%3D100)
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,
![25^2=14^2+20^2](https://tex.z-dn.net/?f=25%5E2%3D14%5E2%2B20%5E2)
![625=196+400](https://tex.z-dn.net/?f=625%3D196%2B400)
![625\neq 596](https://tex.z-dn.net/?f=625%5Cneq%20596)
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,
![10^2=7^2+8^2](https://tex.z-dn.net/?f=10%5E2%3D7%5E2%2B8%5E2)
![100=49+64](https://tex.z-dn.net/?f=100%3D49%2B64)
![100\neq 113](https://tex.z-dn.net/?f=100%5Cneq%20113)
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,
![6^2=3^2+5^2](https://tex.z-dn.net/?f=6%5E2%3D3%5E2%2B5%5E2)
![36=9+25](https://tex.z-dn.net/?f=36%3D9%2B25)
![36\neq 34](https://tex.z-dn.net/?f=36%5Cneq%2034)
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.