If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what type of triangle

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Question: If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

This triangle is a right triangle because it satisfies the Pythagorean theorem: 6^2 + 8^2 = 10^2 (36 + 64 = 100).

If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what type of triangle is it?

If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what type of triangle is it?

Step 1: Identify the lengths of the sides of the triangle. They are 6 cm, 8 cm, and 10 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right 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 10 cm.
Step 4: Calculate the square of each side: 6^2 = 36, 8^2 = 64, and 10^2 = 100.
Step 5: Add the squares of the two shorter sides: 36 + 64 = 100.
Step 6: Compare the sum with the square of the longest side: 100 = 100.
Step 7: Since the equation holds true, conclude that this triangle is a right triangle.

Triangle Classification – Understanding how to classify triangles based on their side lengths and the Pythagorean theorem.
Pythagorean Theorem – Applying the theorem (a^2 + b^2 = c^2) to determine if a triangle is a right triangle.