Question

Question 5
In the figure, if parallelogram ABCD and rectangle ABEM are of equal area, then?


A) Perimeter of ABCD = Perimeter of ABEM
B) Perimeter of ABCD < Perimeter of ABEM
C) Perimeter of ABCD > Perimeter of ABEM
D) Perimeter of ABCD = $\frac{1}{2}$(Perimeter of ABEM)

Answer 1

The correct option is C.

In rectangle ABEM, AB = EM
In parallelogram ABCD, CD = AB

On adding both equations we get,
$AB+CD=EM+AB$

We know, that the perpendicular distance between two parallel sides of a parallelogram is always less than the length of the other parallel sides.

$\therefore BE<BCandAM<AD$
[Since, in a right angle triangle, the hypotenuse is greater than the other side]

On adding both the above inequalities, we get
$BE+AM<BC+AD$
or
$BC+AD>BE+AM$

On adding AB + CD on both sides, we get,

$(AB+CD+BC+AD)>(AB+CD+BE+AM)$

$\Rightarrow (AB+BC+CD+AD)>(EM+AB+BE+AM)$

$[CD=AB=EM]$

$\therefore$ Perimeter of parallelogram ABCD > perimeter of rectangle ABEM