If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

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Question: If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Options:

Correct Answer: Yes

Solution:

Check using the Pythagorean theorem: 25² = 7² + 24², 625 = 49 + 576, 625 = 625. It is a right triangle.

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

If a triangle has sides of lengths 7, 24, and 25, is it 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. The longest side is 25.
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: 625 (from the longest side) equals 625 (from the sum of the other two sides).
Step 8: Since both sides are equal, 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.