Question

In the figure parallelogram FAST and rectangle BASE are on the same base AS and have equal areas.
Which of the following statement is true for parallelogram FAST and rectangle BASE?

• A. They have equal perimeter.
• B. Perimeter of rectangle is greater than that of parallelogram.
• C. Perimeter of parallelogram is greater than that of rectangle.
• D. Perimeter of parallelogram is smaller than that of rectangle.

Answer 1

The correct option is C Perimeter of parallelogram is greater than that of rectangle.


Given: BASE is a rectangle.
In$△ABF$
$\Rightarrow \angle ABF=90°$
AF = Hypotenuse
$\Rightarrow AF>AB$
Similarly, $ST>SE$

In parallelogram FAST:
AS = BE = FT

Perimeter of rectangle = BA+AS+SE+EB
Perimeter of parellelogram = FA+AS+ST+TF

But AF > AB and ST > SE. AF and ST are the sides of the parallelogram.

$\therefore$ Perimeter of Parallelogram is greater than that of rectangle.