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

To determine the type of triangle formed by sides measuring 5 cm, 12 cm, and 13 cm, we can use the Pythagorean theorem. This theorem 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 lengths of the other two sides.

Here, we take the longest side, which is 13 cm, and check if it satisfies the Pythagorean theorem:

1. Calculate the square of the lengths of the sides:

• (5^2 = 25)

• (12^2 = 144)

• (13^2 = 169)

2. According to the theorem, for a right triangle, the equation should hold true:

[

5^2 + 12^2 = 13^2

]

This simplifies to:

[

25 + 144 = 169

]

[

169 = 169

]

Since the equation holds true, this indicates that the triangle with sides 5 cm, 12 cm, and 13 cm is a