Question

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

Answer 1

The sides with lengths of 3cm, 4cm, and 5cm satisfy the Pythagorean Theorem — 3² + 4² equals 5² — confirming that these lengths form a right triangle.

Step-by-step explanation:

To determine if the sides with lengths of 3cm, 4cm, and 5cm form a right triangle, we use the Pythagorean Theorem which states that in a right triangle the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse). The theorem is expressed as a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

Let's apply the theorem with the given lengths:

• Leg a = 3cm
• Leg b = 4cm
• Hypotenuse c = 5cm

We substitute these values into the equation:

3² + 4² = 5²

which simplifies to:

9 + 16 = 25

Since 9 + 16 equals 25, which is the square of 5, the equation holds true. Therefore, the sides 3cm, 4cm, and 5cm do indeed form a right triangle.