In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle

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Question: In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

It is a right triangle because 6^2 + 8^2 = 36 + 64 = 100 = 10^2.

In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle is it?

In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle is it?

Step 1: Identify the lengths of the sides of triangle PQR. They are PQ = 6 cm, QR = 8 cm, and PR = 10 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side in triangle PQR. Here, PR = 10 cm is the longest side.
Step 4: Calculate the square of each side: PQ^2 = 6^2 = 36, QR^2 = 8^2 = 64, and PR^2 = 10^2 = 100.
Step 5: Add the squares of the two shorter sides: 36 + 64 = 100.
Step 6: Compare the sum with the square of the longest side: 100 = 100.
Step 7: Since the sum of the squares of the two shorter sides equals the square of the longest side, triangle PQR is a right triangle.

Pythagorean Theorem – The theorem states that 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.
Triangle Classification – Triangles can be classified based on their side lengths (scalene, isosceles, equilateral) and angles (acute, right, obtuse).