Question: In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a right triangle?
Options:
Yes
No
Cannot be determined
Only if angle G is 90 degrees
Correct Answer: Yes
Solution:
Yes, because 9² + 12² = 81 + 144 = 225 = 15², satisfying the Pythagorean theorem.
In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a rig
Practice Questions
Q1
In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a right triangle?
Yes
No
Cannot be determined
Only if angle G is 90 degrees
Questions & Step-by-Step Solutions
In triangle GHI, if GH = 9 cm, HI = 12 cm, and GI = 15 cm, is triangle GHI a right triangle?
Step 1: Identify the lengths of the sides of triangle GHI. GH = 9 cm, HI = 12 cm, and GI = 15 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Determine which side is the longest. Here, GI (15 cm) is the longest side.
Step 4: Calculate the square of each side: GH² = 9² = 81, HI² = 12² = 144, and GI² = 15² = 225.
Step 5: Add the squares of the two shorter sides: 81 + 144 = 225.
Step 6: Compare the sum from Step 5 to the square of the longest side: 225 (from Step 5) equals 225 (GI²).
Step 7: Since the sum of the squares of the two shorter sides equals the square of the longest side, triangle GHI is a right triangle.
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.
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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