In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a rig
Practice Questions
Q1
In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a right triangle?
Yes
No
Not enough information
Only if angle J is 90 degrees
Questions & Step-by-Step Solutions
In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, is triangle JKL a right triangle?
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 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 in triangle JKL. Here, JL = 13 cm is the longest side.
Step 4: Calculate the square of the lengths of the two shorter sides: JK^2 = 5^2 = 25 and KL^2 = 12^2 = 144.
Step 5: Add these two results together: 25 + 144 = 169.
Step 6: Calculate the square of the longest side: JL^2 = 13^2 = 169.
Step 7: Compare the two results from Step 5 and Step 6. Since 169 = 169, the condition of the Pythagorean theorem is satisfied.
Step 8: Conclude that triangle JKL is a right triangle.
