If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangl

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Question: If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle? (2022)

Options:

Correct Answer: Yes

Exam Year: 2022

Solution:

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle? (2022)

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle? (2022)

Step 1: Identify the lengths of the sides of the triangle. They are 5 cm, 12 cm, and 13 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. Here, the longest side is 13 cm.
Step 4: Calculate the square of the longest side: 13 cm squared is 13² = 169.
Step 5: Calculate the squares of the other two sides: 5 cm squared is 5² = 25 and 12 cm squared is 12² = 144.
Step 6: Add the squares of the two shorter sides: 25 + 144 = 169.
Step 7: Compare the sum from Step 6 with the square of the longest side from Step 4: 169 = 169.
Step 8: Since both sides are equal, conclude that the triangle is a right triangle.

Pythagorean Theorem – A theorem stating 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.