The set of side lengths that form a right triangle is 7, 24, 25
Explanation:
We can solve this using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2. We can plug each set of numbers into the equation, one by one, to see if the set of numbers is true in the equation. One thing to note is that the largest number out of the set is always the hypotenuse, or c. The other numbers are the legs (a and b.)
5, 11, 13
a^2 + b^2 = c^2
(5)^2 + (11)^2 = (13)^2
25 + 121 = 169
146 ≠ 169
Since 146 doesn't equal 169, this is NOT a right triangle
9, 24, 25
a^2 + b^2 = c^2
(9)^2 + (24)^2 = (25)^2
81 + 576 = 625
657 ≠ 625
Since 657 doesn't equal 625, this is NOT a right triangle
7, 24, 25
a^2 + b^2 = c^2
(7)^2 + (24)^2 = (25)^2
49 + 576 = 625
625 = 625
This equation is true, because 625 = 625. Therefore this IS a right triangle.
