In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of t

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Question: In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)

Options:

Correct Answer: Right-angled

Exam Year: 2023

Solution:

Since 5² + 12² = 13² (25 + 144 = 169), triangle JKL is a right-angled triangle.

In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)

In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)

Step 1: Identify the lengths of the sides of triangle JKL. They are JK = 5 cm, KL = 12 cm, and JL = 13 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Step 3: Identify the longest side, which is JL = 13 cm. This will be our hypotenuse.
Step 4: Calculate the squares of the lengths of the sides: JK² = 5² = 25, KL² = 12² = 144, and JL² = 13² = 169.
Step 5: Add the squares of the two shorter sides: 5² + 12² = 25 + 144 = 169.
Step 6: Compare the sum with the square of the hypotenuse: 169 (from JK² + KL²) equals 169 (from JL²).
Step 7: Since the equation holds true (5² + 12² = 13²), triangle JKL is a right-angled triangle.

Pythagorean Theorem – The theorem states that in a right-angled 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.
Triangle Classification – Triangles can be classified based on their side lengths and angles, including right-angled, acute, and obtuse triangles.