In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a righ

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Question: In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, if PQ² + PR² = QR², then it is a right triangle. 8² + 6² = 64 + 36 = 100 = 10².

In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a right triangle?

In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a right triangle?

Step 1: Identify the lengths of the sides of triangle PQR. We have PQ = 8 cm, PR = 6 cm, and QR = 10 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 = 10 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: PQ² = 8² = 64, PR² = 6² = 36, and QR² = 10² = 100.
Step 5: Add the squares of the two shorter sides: PQ² + PR² = 64 + 36 = 100.
Step 6: Compare the sum from Step 5 with the square of the hypotenuse: QR² = 100.
Step 7: Since PQ² + PR² = QR² (100 = 100), triangle PQR is a right triangle.

Pythagorean Theorem – In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.