In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of t

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Question: In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)

Options:

Correct Answer: Right-angled

Exam Year: 2023

Solution:

Using the Pythagorean theorem, 8² + 15² = 64 + 225 = 289 = 17². Hence, it is a right-angled triangle.

In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)

In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)

Step 1: Identify the lengths of the sides of triangle MNO. They are MN = 8 cm, NO = 15 cm, and MO = 17 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right-angled 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, which is MO = 17 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: MN² = 8² = 64, NO² = 15² = 225, and MO² = 17² = 289.
Step 5: Add the squares of the two shorter sides: 64 + 225 = 289.
Step 6: Compare this sum to the square of the hypotenuse: 289 = 289.
Step 7: Since the equation holds true, we conclude that triangle MNO is a right-angled triangle.

Pythagorean Theorem – A mathematical principle used to determine if a triangle is right-angled by checking if the square of the longest side equals the sum of the squares of the other two sides.
Triangle Classification – Understanding the different types of triangles (e.g., right, acute, obtuse) based on the lengths of their sides.