Triangle Medians and Inequality Statements
CMAT 2024 · Quantitative Techniques & Data Interpretation · Medium · Geometry
Given below are two statements : Statement I: The perimeter of a triangle is greater than the sum of its three medians. Statement II: In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2 AD. In the light of the above statements, choose the correct answer from the options given below :
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
A
Explanation
Statement I is true: The sum of the lengths of the medians of a triangle is always less than the perimeter. Statement II is true: In , . In , . Adding both inequalities gives .
Related Geometry questions
- #2866Equal Area Shapes ComparisonCMATQTDIMCQEasy
- #3054Area of Equilateral Triangle with Inradius RCMATQTDIMCQEasy
- #3148Geometry of Right Angled Triangle AreaCMATQTDIMCQHard
- #3243Perpendicular in TriangleCMATQTDIMCQMedium
- #3344Farthest distance on cylinderCMATQTDIMCQEasy
- #3361Valid triangle side lengthsCMATQTDIMCQEasy
- #3442Angle bisector theoremCMATQTDIMCQEasy
- #3533Angle in an isosceles triangle formed by circle radiiCMATQTDIMCQEasy
Practise this under exam conditions
Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.
Solve in the workspace