If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, what type of triangle

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

Options:

Correct Answer: Right

Solution:

This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).

If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, what type of triangle is it?

If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, what type of triangle is it?

Step 1: Identify the lengths of the sides of the triangle. They are 7 cm, 24 cm, and 25 cm.
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. Here, the longest side is 25 cm.
Step 4: Calculate the square of each side: 7² = 49, 24² = 576, and 25² = 625.
Step 5: Add the squares of the two shorter sides: 49 + 576 = 625.
Step 6: Compare the sum with the square of the longest side: 625 (from the sum) equals 625 (from 25²).
Step 7: Since the equation 7² + 24² = 25² holds true, this means the triangle is a right triangle.

Pythagorean Theorem – A theorem 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 Classification – Triangles can be classified based on their side lengths (scalene, isosceles, equilateral) and angles (acute, right, obtuse).