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

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

Options:

Correct Answer: 10 cm

Solution:

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

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

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

Step 1: Identify the triangle PQR where angle P is 90 degrees, making it a right triangle.
Step 2: Note the lengths of the two sides that form the right angle: PQ = 6 cm and PR = 8 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 lengths 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 = 6² + 8².
Step 6: Calculate the squares: 6² = 36 and 8² = 64.
Step 7: Add the squares together: 36 + 64 = 100.
Step 8: Take the square root of 100 to find QR: QR = √100.
Step 9: Calculate the square root: QR = 10 cm.

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