2024 · Q67
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. A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD. Question : What is the perimeter of the quadrilateral ?
Statement IAB + DC = 10 cm
Statement IIAD + BC = 10 cm
Elementary MathematicsQuadrilaterals and Polygons
- 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
A quadrilateral circumscribing a circle is tangential, so AB + CD = AD + BC and the perimeter is twice either sum. Statement I gives 2 × 10 = 20 cm and statement II independently gives 2 × 10 = 20 cm. Either alone suffices: option (b).