In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of t
Practice Questions
Q1
In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)
Equilateral
Isosceles
Scalene
Right-angled
Questions & Step-by-Step Solutions
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.
