In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectiv

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Question: In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.

In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?

In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?

Step 1: Identify the lengths of the sides of triangle ABC. Here, side a = 7, side b = 24, and side c = 25.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side. In this case, side c (25) is the longest side.
Step 4: Calculate the square of each side: a² = 7² = 49, b² = 24² = 576, and c² = 25² = 625.
Step 5: Add the squares of sides a and b: 49 + 576 = 625.
Step 6: Compare the sum from Step 5 with the square of side c: 625 = 625.
Step 7: Since the equation from Step 6 is true, triangle ABC is a right triangle.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Triangle Classification – Triangles can be classified based on their side lengths and angles, including right, acute, and obtuse triangles.