In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the

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Question: In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)

Options:

Correct Answer: 15 cm

Exam Year: 2022

Solution:

Using the Pythagorean theorem, GI = √(HI² - GH²) = √(12² - 9²) = √(144 - 81) = √63 = 15 cm.

In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)

In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)

Step 1: Identify the triangle GHI. We know that angle G is 90 degrees, which means it is a right triangle.
Step 2: Label the sides of the triangle. GH is one side (9 cm), HI is the other side (12 cm), and we need to find the length of side GI.
Step 3: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 4: In our triangle, GI is the hypotenuse, and GH and HI are the other two sides.
Step 5: According to the Pythagorean theorem, we can write the equation: GI² = GH² + HI².
Step 6: Substitute the known values into the equation: GI² = 9² + 12².
Step 7: Calculate the squares: 9² = 81 and 12² = 144.
Step 8: Add the squares together: GI² = 81 + 144 = 225.
Step 9: To find GI, take the square root of 225: GI = √225.
Step 10: Calculate the square root: GI = 15 cm.

Pythagorean Theorem – In a right triangle, the square of the length of the hypotenuse (GI) is equal to the sum of the squares of the lengths of the other two sides (GH and HI).