If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle i

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Question: If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it? (2022)

Options:

Correct Answer: Right-angled

Exam Year: 2022

Solution:

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right-angled triangle.

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it? (2022)

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it? (2022)

Step 1: Identify the lengths of the sides of the triangle. They are 3 cm, 4 cm, and 5 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side. In this case, the longest side is 5 cm.
Step 4: Calculate the square of each side: 3² = 9, 4² = 16, and 5² = 25.
Step 5: Add the squares of the two shorter sides: 9 + 16 = 25.
Step 6: Compare the sum with the square of the longest side: 25 (from the shorter sides) equals 25 (from the longest side).
Step 7: Since the equation 3² + 4² = 5² holds true, the triangle is a right-angled triangle.

Triangle Classification – Understanding how to classify triangles based on their side lengths and angles, particularly using the Pythagorean theorem for right-angled triangles.
Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.