In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, what type of triangle

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Question: In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

Using the Pythagorean theorem, 7² + 24² = 49 + 576 = 625 = 25², thus triangle PQR is a right triangle.

In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, what type of triangle is it?

In triangle PQR, if PQ = 7 cm, PR = 24 cm, and QR = 25 cm, what type of triangle is it?

Step 1: Identify the lengths of the sides of triangle PQR. They are PQ = 7 cm, PR = 24 cm, and QR = 25 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Step 3: Identify the longest side, which is QR = 25 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: PQ² = 7² = 49, PR² = 24² = 576, and QR² = 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 hypotenuse: 625 = 625.
Step 7: Since the equation holds true, triangle PQR is a right triangle.

Pythagorean Theorem – A fundamental principle in geometry 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 and angles, including right, acute, and obtuse triangles.