In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then

Options

A. perimeter of ABCD = perimeter of ABEM
B. perimeter of `ABCD lt` perimeter of ABEM
C. perimeter of `ABCD gt` perimeter of ABEM
D. perimeter of `ABCD = (1)/(2)` (perimeter of ABEM)

Answer

C

Explanation

In rectangle ABEM, `" "AB = EM" "` [sides of rectangle]
and in parallelogram ABCD, CD = AB
On adding, both equations, we get
`AB + CD = EM + AB" "` ...(i)
We know that, the perpandicular distance between two parallel sides of a parallelogram is always less then the length of the other parallel sides.
`therefore` `BE lt BC " and " AM lt AD`
[since, in a right angled triangle, the hypotenuse is greater than the other sides]
On adding both above inequalities, we get
`BE + AM lt BC + AD " or " BC + AD gt BE + AM`
On adding AB+CD both sides, we get
`AB + CD + BC + AD gt AB + CD + BE + AM`
`rArr" "` `AB + BC + CD + AD gt AB + BE + EM + AM" "` `[because CD = AB = EM]`
`therefore" "` Perimeter of parallelogram `ABCD gt` perimeter of rectangle ABEM