2014 · Q82
Consider the following statements:
- 1Let ABCD be a parallelogram which is not a rectangle. Then 2(AB^2 + BC^2) ≠ AC^2 + BD^2.
- 2If ABCD is a rhombus with AB = 4 cm, then AC^2 + BD^2 = n^3 for some positive integer n.
Which of the above statements is/are correct?
Elementary MathematicsGeometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Parallelogram law gives 2(AB^2+BC^2) = AC^2+BD^2 always, so 1 is false; for a rhombus AC^2+BD^2 = 4(4^2) = 64 = 4^3, so 2 is true.