Answer:
Right triangle.
Step-by-step explanation:
Side lengths 9, 12, and 15 form a right triangle.
According to the Converse of the Pythagorean Theorem, If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
Let a = 9
b = 12
c = 15
We'll plug in these values into the Pythagorean Theorem to determine whether the squared value of the longest side is equal to the sum of the squared value of the two other sides:
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]15^{2} = 9^{2} + 12^{2}[/tex]
225 = 81 + 144
225 = 225
Since the sum of the squared lengths of the two other sides is equal to the squared value of the longest side, then it means that it is a right triangle.
