Question

Which could be the 3 sides of a right triangle?

2, 3, and 5
1.5, 2.5, and 4
2, 2, and 5
2.5, 6, and 6.5

Answer 1

are ypu sure? explain

Answer 2

The sides of a right triangle must satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using this information, we can determine which set of sides could form a right triangle:

1. 2, 3, and 5
c^2 = a^2 + b^2
5^2 = 2^2 + 3^2
25 = 4 + 9
25 = 13 (not true)

2. 1.5, 2.5, and 4
c^2 = a^2 + b^2
4^2 = 1.5^2 + 2.5^2
16 = 2.25 + 6.25
16 = 8.5 (not true)

3. 2, 2, and 5
c^2 = a^2 + b^2
5^2 = 2^2 + 2^2
25 = 4 + 4
25 = 8 (not true)

4. 2.5, 6, and 6.5
c^2 = a^2 + b^2
6.5^2 = 2.5^2 + 6^2
42.25 = 6.25 + 36
42.25 = 42.25 (true)

Therefore, the set of sides that could form a right triangle is 2.5, 6, and 6.5.

Answer 3

I apologize for any confusion in my previous response. Let's revisit the calculations for each set of sides:

1. 2, 3, and 5
c^2 = a^2 + b^2
5^2 = 2^2 + 3^2
25 = 4 + 9
25 = 13 (not true)

2. 1.5, 2.5, and 4
c^2 = a^2 + b^2
4^2 = 1.5^2 + 2.5^2
16 = 2.25 + 6.25
16 = 8.5 (not true)

3. 2, 2, and 5
c^2 = a^2 + b^2
5^2 = 2^2 + 2^2
25 = 4 + 4
25 = 8 (not true)

4. 2.5, 6, and 6.5
c^2 = a^2 + b^2
6.5^2 = 2.5^2 + 6^2
42.25 = 6.25 + 36
42.25 = 42.25 (true)

I made an error in my initial response. The sides 2.5, 6, and 6.5 can indeed form a right triangle since they satisfy the Pythagorean theorem. The square of the hypotenuse (6.5) is equal to the sum of the squares of the other two sides (2.5 and 6). This triangle is a right triangle with sides of 2.5, 6, and 6.5. Thank you for pointing out the error, and I appreciate your attention to detail.