In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what i

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Question: In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?

Options:

Correct Answer: Right

Solution:

Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.

In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?

In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?

Step 1: Identify the lengths of the sides of triangle ABC. They are 10 cm, 24 cm, and 26 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 26 cm.
Step 4: Calculate the square of the lengths of the two shorter sides: 10 cm and 24 cm.
Step 5: Calculate 10 squared: 10² = 100.
Step 6: Calculate 24 squared: 24² = 576.
Step 7: Add the squares of the two shorter sides: 100 + 576 = 676.
Step 8: Calculate the square of the longest side: 26² = 676.
Step 9: Compare the results from Step 7 and Step 8. Since 100 + 576 = 676 and 26² = 676, they are equal.
Step 10: Conclude that triangle ABC is a right triangle because the Pythagorean theorem holds true.

Pythagorean Theorem – The theorem states 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.
Types of Triangles – Triangles can be classified based on their angles (acute, right, obtuse) or their sides (scalene, isosceles, equilateral).