In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the

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Question: In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the length of QR?

Options:

Correct Answer: 10 cm

Solution:

Using the Pythagorean theorem, QR = √(PQ² + PR²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.

In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the length of QR?

In triangle PQR, if PQ = 8 cm, PR = 6 cm, and angle P = 90 degrees, what is the length of QR?

Step 1: Identify the triangle PQR where angle P is 90 degrees. This means it is a right triangle.
Step 2: Note the lengths of the sides: PQ = 8 cm and PR = 6 cm.
Step 3: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (QR) is equal to the sum of the squares of the other two sides (PQ and PR).
Step 4: Write the formula: QR² = PQ² + PR².
Step 5: Substitute the values into the formula: QR² = 8² + 6².
Step 6: Calculate 8², which is 64, and 6², which is 36.
Step 7: Add these two results together: 64 + 36 = 100.
Step 8: Take the square root of 100 to find QR: QR = √100.
Step 9: Calculate the square root of 100, which is 10 cm.
Step 10: Conclude that the length of QR is 10 cm.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse (QR) is equal to the sum of the squares of the lengths of the other two sides (PQ and PR).