2024 · Q32
If p, q and r are the lengths (in cm) of the sides of a right-angled triangle, then (p - q - r) (q - r - p) (r - p - q) is always
Elementary MathematicsGeometry: Lines, Angles and Triangles
- APositive only
- BNegative only
- CNon-positive only
- DNon-negative only
Explanation
Let r be the hypotenuse. Each factor is a side minus the sum of the other two, e.g. p−q−r < 0 since p < q+r in any triangle. All three factors are negative, so their product is negative — option B ('Negative only').