If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a ri

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Question: If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a right triangle? (2023)

Options:

Correct Answer: Yes

Exam Year: 2023

Solution:

Using Pythagoras theorem, 7² + 24² = 49 + 576 = 625 = 25², so it is a right triangle.

If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a right triangle? (2023)

If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a right triangle? (2023)

Step 1: Identify the lengths of the sides of the triangle. They are 7 cm, 24 cm, and 25 cm.
Step 2: Recognize that for a triangle to be a right triangle, it must satisfy the Pythagorean theorem, which states that a² + b² = c², where c is the longest side.
Step 3: Determine which side is the longest. Here, 25 cm is the longest side.
Step 4: Assign the sides: let a = 7 cm, b = 24 cm, and c = 25 cm.
Step 5: Calculate a² (7²) which equals 49.
Step 6: Calculate b² (24²) which equals 576.
Step 7: Calculate c² (25²) which equals 625.
Step 8: Add a² and b² together: 49 + 576 = 625.
Step 9: Compare the sum of a² and b² to c²: 625 equals 625.
Step 10: Since a² + b² equals c², conclude that the triangle is a right triangle.

Pythagorean Theorem – A mathematical principle stating that 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 – A principle that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.