In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a righ
Practice Questions
Q1
In triangle PQR, if PQ = 8 cm, PR = 6 cm, and QR = 10 cm, is triangle PQR a right triangle?
Yes
No
Cannot be determined
Only if angle P is 90 degrees
Questions & Step-by-Step Solutions
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.
