Question

"Given the side lengths √9, √25, and 4, determine whether these lengths form a right triangle. Additionally, check if this set of side lengths constitutes a Pythagorean triple."

Answer 1

The side lengths √9 (3), √25 (5), and 4 do form a right triangle because they satisfy the Pythagorean theorem: 3² + 4² = 5². Also, these lengths are a Pythagorean triple.

Step-by-step explanation:

To determine whether the side lengths √9, √25, and 4 form a right triangle, and if these side lengths are a Pythagorean triple, we need to use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be represented as a² + b² = c². Let's calculate the lengths:

• √9 = 3
• √25 = 5
• 4 (already a whole number)

Now compare the squares of these lengths:

3² + 4² = 9 + 16 = 25

5² = 25

Since the sum of the squares of the two smaller sides equals the square of the largest side, these lengths satisfy the Pythagorean theorem and form a right triangle. Furthermore, since the sides are whole numbers, these lengths constitute a Pythagorean triple.