In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of t
Practice Questions
Q1
In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)
Equilateral
Isosceles
Scalene
Right-angled
Questions & Step-by-Step Solutions
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.
