To determine if a set of three sides will form a right triangle, we can use the Pythagorean theorem, which states that in a right 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.
Let's check each set of sides:
1. 3, 7, 12:
3^2 + 7^2 = 9 + 49 = 58
12^2 = 144
Since 58 is not equal to 144, this set does not form a right triangle.
2. 9, 6, 12:
9^2 + 6^2 = 81 + 36 = 117
12^2 = 144
Again, 117 is not equal to 144, so this set does not form a right triangle.
3. 18, 10, 8:
18^2 + 10^2 = 324 + 100 = 424
8^2 = 64
Once again, 424 is not equal to 64, so this set does not form a right triangle.
4. 15, 8, 17:
15^2 + 8^2 = 225 + 64 = 289
17^2 = 289
In this case, 289 is equal to 289, which means this set does form a right triangle.
Therefore, the set of sides 15, 8, and 17 will form a right triangle.
Given the three sides of a triangle, which set will form a right triangle?
3, 7, 12
9, 6, 12
18, 10, 8
15, 8, 17
1 answer
2 answers