Consider the following for the next ten (10) items that follow: Each item contains a Question followed by two Statements. Answer each item using the following instructions: Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly not a rectangle) with adjacent sides of length x and y is Q. Question : What is the ratio of the lengths of diagonals of a rhombus ?
- AIf the Question can be answered by one of the Statements alone, but not by the other.
- BIf the Question can be answered by either Statement alone.
- CIf the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DIf the Question cannot be answered even by using both Statements together.
Explanation
Statement I: a diagonal equal to the side splits the rhombus into two equilateral triangles, so the half-diagonals are s/2 and s√3/2 — ratio 1 : √3. Statement II: with the longer diagonal √3 times the side (as printed; a literal “3 times” would be geometrically impossible since a diagonal is shorter than twice the side), the same 1 : √3 ratio follows. Either statement alone determines the ratio: option (b).