A triangle has sides of lengths 7, 24, and 25. Is this triangle a right triangle

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Question: A triangle has sides of lengths 7, 24, and 25. Is this triangle a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, check if 25² = 7² + 24². 625 = 49 + 576, which is true. Thus, it is a right triangle.

A triangle has sides of lengths 7, 24, and 25. Is this triangle a right triangle?

A triangle has sides of lengths 7, 24, and 25. Is this triangle a right triangle?

Step 1: Identify the lengths of the sides of the triangle. They are 7, 24, and 25.
Step 2: Determine which side is the longest. Here, 25 is the longest side.
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides.
Step 4: Calculate the square of the longest side: 25² = 625.
Step 5: Calculate the square of the other two sides: 7² = 49 and 24² = 576.
Step 6: Add the squares of the two shorter sides: 49 + 576 = 625.
Step 7: Compare the results from Step 4 and Step 6: 625 = 625.
Step 8: Since both sides are equal, conclude that the triangle is a right triangle.

Pythagorean Theorem – A mathematical principle that states 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.