In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of

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Question: In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of triangle? (2023)

Options:

Correct Answer: Right-angled

Exam Year: 2023

Solution:

Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.

In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of triangle? (2023)

In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of triangle? (2023)

Step 1: Identify the lengths of the sides of triangle JKL. They are JK = 15 cm, KL = 20 cm, and JL = 25 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 = 25 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: JK² = 15² = 225, KL² = 20² = 400, and JL² = 25² = 625.
Step 5: Add the squares of the two shorter sides: 225 + 400 = 625.
Step 6: Compare the sum with the square of the hypotenuse: 625 (sum of JK² and KL²) equals 625 (JL²).
Step 7: Since the equation holds true (15² + 20² = 25²), 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 (scalene, isosceles, equilateral) and angles (acute, right, obtuse).