In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, is triangle PQR a rig

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Question: In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, is triangle PQR a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2, so triangle PQR is a right triangle.

In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, is triangle PQR a right triangle?

In triangle PQR, if PQ = 5 cm, QR = 12 cm, and PR = 13 cm, is triangle PQR a right triangle?

Step 1: Identify the lengths of the sides of triangle PQR. They are PQ = 5 cm, QR = 12 cm, and PR = 13 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 PR = 13 cm. This will be our hypotenuse.
Step 4: Calculate the square of the lengths of the two shorter sides: PQ^2 = 5^2 = 25 and QR^2 = 12^2 = 144.
Step 5: Add these two results together: 25 + 144 = 169.
Step 6: Now calculate the square of the hypotenuse: PR^2 = 13^2 = 169.
Step 7: Compare the two results: 169 (from the sum of the squares of the shorter sides) is equal to 169 (the square of the hypotenuse).
Step 8: Since both sides are equal, 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.