2012 · Q45
ABCD is a rectangle. Let E be a point on AB and F a point on CD such that DE is parallel to BF. If AE = 3 cm and if the area of triangle BFC = 6 square cm. Consider the following statements:
- 1Area of rectangle ABCD can be of the form pq^2 square cm where p, q are distinct primes.
- 2Area of the figure EBFD is of the form r^2 square cm where r is rational but not an integer.
Which of the above statements is/are correct?
Elementary MathematicsGeometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Area BFC = 6 gives height 4 cm with FC = 3 cm; the width is free, so the area 4w can be pq^2 (statement 1 true), but the area of EBFD = 4(w-3) is not necessarily a perfect square (statement 2 false).