Question

A triangle has sides with lengths of 3 cm, 4 cm, and 5 cm. Substitute these values into the Pythagorean Theorem to determine if the sides form a right triangle.

Answer 1

The sides (3 cm, 4 cm, and 5 cm) form a right triangle.

Step-by-step explanation:

To determine if the sides form a right triangle, we can substitute the lengths of the sides (3 cm, 4 cm, and 5 cm) into the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (hypotenuse).

Using the Pythagorean Theorem, we can calculate:

a2 + b2 = c2

Substituting the known side lengths:

32 + 42 = 52

Simplifying:

9 + 16 = 25

Therefore, the sum of the squares of the two shorter sides (9 and 16) is equal to the square of the longest side (25).

Since the equation holds true, the sides (3 cm, 4 cm, and 5 cm) do form a right triangle.