A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle?

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Question: A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? (2019)

Options:

Correct Answer: Yes

Exam Year: 2019

Solution:

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

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? (2019)

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? (2019)

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 the longest side: 25^2 = 625.
Step 5: Calculate the squares 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 sum from Step 6 with the square of the longest side from Step 4: 625 = 625.
Step 8: Since both sides are equal, conclude that the triangle 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.
Triangle Classification – Understanding how to classify triangles based on their side lengths and angles, particularly distinguishing between right, acute, and obtuse triangles.