In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a righ

₹0.0

Question: In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, 7² + 5² = 49 + 25 = 74, and 10² = 100. Since 74 ≠ 100, triangle GHI is not a right triangle.

In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a right triangle?

In triangle GHI, if GH = 7 cm, HI = 10 cm, and GI = 5 cm, is triangle GHI a right triangle?

Step 1: Identify the lengths of the sides of triangle GHI. They are GH = 7 cm, HI = 10 cm, and GI = 5 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, HI (10 cm) is the longest side.
Step 4: Calculate the squares of the lengths of the sides: GH² = 7² = 49, GI² = 5² = 25, and HI² = 10² = 100.
Step 5: Add the squares of the two shorter sides: 49 + 25 = 74.
Step 6: Compare the sum of the squares of the two shorter sides (74) with the square of the longest side (100).
Step 7: Since 74 is not equal to 100, triangle GHI does not satisfy the Pythagorean theorem.
Step 8: Conclude that triangle GHI is not a right triangle.

Pythagorean Theorem – A mathematical principle used to determine if a triangle is a right triangle by checking if the square of the longest side equals the sum of the squares of the other two sides.