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

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

Options:

Correct Answer: Scalene

Solution:

Since all sides are of different lengths, triangle PQR is a scalene triangle.

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

In triangle PQR, if PQ = 8 cm, QR = 6 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 = 8 cm, QR = 6 cm, and PR = 10 cm.
Step 2: Check if all sides are different lengths. Compare PQ, QR, and PR.
Step 3: Since 8 cm (PQ), 6 cm (QR), and 10 cm (PR) are all different, we conclude that the triangle has no equal sides.
Step 4: Based on the definition of triangle types, a triangle with all sides of different lengths is called a scalene triangle.
Step 5: Therefore, triangle PQR is a scalene triangle.

Triangle Classification – Triangles can be classified based on the lengths of their sides: scalene (all sides different), isosceles (two sides equal), and equilateral (all sides equal).
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.