Triangle ABC has side lengths 7, 24, and 25. Do the side lengths form a Pythagorean triple? Explain.
Thank You so much! :) I'm having a hard time understanding this so it means alot!
Yes, they do. You can read about Pythagorean triples for an explanation.
Wait then is it B?
To determine if the side lengths 7, 24, and 25 form a Pythagorean triple, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, let's label the sides of the triangle:
Side A = 7
Side B = 24
Side C (hypotenuse) = 25
Now, we can calculate the squares of each side:
A^2 = 7^2 = 49
B^2 = 24^2 = 576
C^2 = 25^2 = 625
According to the Pythagorean theorem, if the triangle is a right-angled triangle, then A^2 + B^2 should be equal to C^2.
49 + 576 = 625
Since 49 + 576 is equal to 625, we can conclude that the side lengths 7, 24, and 25 do form a Pythagorean triple. Therefore, triangle ABC is a right-angled triangle.
To determine if the side lengths of a triangle form a Pythagorean triple, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides. In this case, 25 is the longest side.
To find the squares of the other two sides, we square 7 and 24.
- The square of 7 is 7^2 = 49.
- The square of 24 is 24^2 = 576.
Now, we need to check if the sum of these two squared values is equal to the square of the longest side:
49 + 576 = 625.
The square of 25 is 25^2 which is also equal to 625.
Since the sum of the squares of the other two sides is equal to the square of the longest side (25), the side lengths 7, 24, and 25 form a Pythagorean triple.
I hope this explanation helps you understand the concept of Pythagorean triples better! Let me know if you have any more questions.