In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the

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Question: In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)

Options:

Correct Answer: 12 cm

Exam Year: 2023

Solution:

Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.

In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)

In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)

Step 1: Identify the triangle JKL where angle J is 90 degrees, making it a right triangle.
Step 2: Note the lengths of the sides: JK = 15 cm (one leg) and KL = 20 cm (the hypotenuse).
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (KL) is equal to the sum of the squares of the other two sides (JK and JL).
Step 4: Write the formula: KL² = JK² + JL².
Step 5: Substitute the known values into the formula: 20² = 15² + JL².
Step 6: Calculate 20² and 15²: 400 = 225 + JL².
Step 7: Rearrange the equation to find JL²: JL² = 400 - 225.
Step 8: Calculate the right side: JL² = 175.
Step 9: Take the square root of both sides to find JL: JL = √175.
Step 10: Simplify √175 to get JL = 12 cm.

Pythagorean Theorem – 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.
Right Triangle Properties – Understanding the properties of right triangles, including the relationship between the sides and angles.