The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this tri

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Question: The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)

Options:

Correct Answer: Yes

Exam Year: 2020

Solution:

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)

The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)

Step 1: Identify the lengths of the sides of triangle ABC. They are 7 cm, 24 cm, and 25 cm.
Step 2: Recognize that in a right triangle, the square of the longest side (hypotenuse) should equal the sum of the squares of the other two sides.
Step 3: Identify the longest side, which is 25 cm.
Step 4: Calculate the square of the longest side: 25^2 = 625.
Step 5: Calculate the square of the other two sides: 7^2 = 49 and 24^2 = 576.
Step 6: Add the squares of the two shorter sides: 49 + 576 = 625.
Step 7: Compare the results: 625 (from the two shorter sides) equals 625 (from the longest side).
Step 8: Since the two results are equal, conclude that triangle ABC 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.