If a triangle has sides measuring 5, 12, and 13, what type of triangle is it?

The triangle with sides measuring 5, 12, and 13 is classified as a right triangle because it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, 13 is the longest side. When we square the lengths of the sides, we get:

• The square of 5 is ( 5^2 = 25 )

• The square of 12 is ( 12^2 = 144 )

• The square of 13 is ( 13^2 = 169 )

Now, according to the Pythagorean theorem, we check whether:

( 5^2 + 12^2 = 13^2 )

Substituting the values, we have:

( 25 + 144 = 169 )

Since both sides of the equation are equal, it confirms that the triangle is indeed a right triangle. Understanding the properties of right triangles is essential for various applications in geometry and real-world scenarios, making this identification particularly important.

The other types of triangles mentioned do not