what set if numbers could be possible side lengths in units of a right triangle a 3,4,5 b 5,5,5 c 5,5,7 d 5,8,10
The set of numbers that could be possible side lengths in units of a right triangle are:
a) 3, 4, 5 - Correct. This is a Pythagorean triple, meaning it satisfies the Pythagorean theorem (a² + b² = c²), where 3² + 4² = 5².
b) 5, 5, 5 - Incorrect. This is not a right triangle since it violates the Pythagorean theorem. (5² + 5² ≠ 5²).
c) 5, 5, 7 - Incorrect. This is also not a right triangle since it violates the Pythagorean theorem. (5² + 5² ≠ 7²).
d) 5, 8, 10 - Correct. This is another Pythagorean triple, which satisfies the Pythagorean theorem where 5² + 8² = 10².
To determine which set of numbers could be possible side lengths in units of a right triangle, we can use the Pythagorean Theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's check each set of numbers:
a) 3, 4, 5:
Using the Pythagorean Theorem:
3^2 + 4^2 = 9 + 16 = 25
5^2 = 25
The equation is satisfied, so the set {3, 4, 5} could be possible side lengths of a right triangle.
b) 5, 5, 5:
Using the Pythagorean Theorem:
5^2 + 5^2 = 25 + 25 = 50
5^2 * 2 = 50
The equation is not satisfied, so the set {5, 5, 5} could not be possible side lengths of a right triangle.
c) 5, 5, 7:
Using the Pythagorean Theorem:
5^2 + 5^2 = 25 + 25 = 50
7^2 = 49
The equation is not satisfied, so the set {5, 5, 7} could not be possible side lengths of a right triangle.
d) 5, 8, 10:
Using the Pythagorean Theorem:
5^2 + 8^2 = 25 + 64 = 89
10^2 = 100
The equation is not satisfied, so the set {5, 8, 10} could not be possible side lengths of a right triangle.
Therefore, the only set of numbers that could be possible side lengths of a right triangle is a) 3, 4, 5.