A triangle has sides measuring 5 cm, 12 cm, and 13 cm. Is this triangle a right triangle?

To determine if a triangle with sides measuring 5 cm, 12 cm, and 13 cm is a right triangle, we can use the Pythagorean theorem. This theorem 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, the longest side is 13 cm. We will check if:

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

Calculating the squares:

• ( 13^2 = 169 )

• ( 5^2 = 25 )

• ( 12^2 = 144 )

Now we add ( 5^2 ) and ( 12^2 ):

( 25 + 144 = 169 )

Since both sides of the equation are equal (169 = 169), the triangle satisfies the condition of the Pythagorean theorem, confirming that it is indeed a right triangle.

Thus, the triangle with sides 5 cm, 12 cm, and 13 cm is a right triangle.