Answer :
To determine if the given set of sides can form a right triangle, we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's check if the sides 5, 12, and 14 can create a right triangle.
1. Identify the sides:
- We have sides: 5, 12, and 14.
- The longest side here is 14, which would be the hypotenuse if these sides form a right triangle.
2. Calculate the squares of the sides:
- Square of 5: [tex]\(5^2 = 25\)[/tex]
- Square of 12: [tex]\(12^2 = 144\)[/tex]
- Square of 14 (hypotenuse): [tex]\(14^2 = 196\)[/tex]
3. Apply the Pythagorean theorem:
- Add the squares of the two shorter sides: [tex]\(25 + 144 = 169\)[/tex]
- Compare this sum with the square of the longest side (hypotenuse): [tex]\(196\)[/tex]
4. Conclusion:
- Since [tex]\(169 \neq 196\)[/tex], the sum of the squares of the two shorter sides (5 and 12) does not equal the square of the longest side (14).
Therefore, the given sides 5, 12, and 14 do not form a right triangle.
Let's check if the sides 5, 12, and 14 can create a right triangle.
1. Identify the sides:
- We have sides: 5, 12, and 14.
- The longest side here is 14, which would be the hypotenuse if these sides form a right triangle.
2. Calculate the squares of the sides:
- Square of 5: [tex]\(5^2 = 25\)[/tex]
- Square of 12: [tex]\(12^2 = 144\)[/tex]
- Square of 14 (hypotenuse): [tex]\(14^2 = 196\)[/tex]
3. Apply the Pythagorean theorem:
- Add the squares of the two shorter sides: [tex]\(25 + 144 = 169\)[/tex]
- Compare this sum with the square of the longest side (hypotenuse): [tex]\(196\)[/tex]
4. Conclusion:
- Since [tex]\(169 \neq 196\)[/tex], the sum of the squares of the two shorter sides (5 and 12) does not equal the square of the longest side (14).
Therefore, the given sides 5, 12, and 14 do not form a right triangle.
