2018 · Q74
Let S be the parallelogram obtained by joining the mid-points of the parallelogram T. Consider the following statements :
- 1The ratio of area of T to that of S is 2 : 1. 2 The perimeter of S is half of the sum of diagonals of T.
Which of the above statementsis/are correct ?
Elementary MathematicsQuadrilaterals and Polygons
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
The Varignon parallelogram joining the midpoints has exactly half the area of T (statement 1 true). Its sides are half the diagonals of T, so its perimeter equals the full sum of the diagonals of T, not half (statement 2 false). Hence option A.