Question

Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show that perimeter of the parallelogram is greater than that of rectangle

Answer 1

hey!

points to be remembered

•no matter how many line segments are drawn the perpendicular will always be the smallest

•a rectangle is also a parallelogram
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ABEF is a rectangle and ABCD is ||gm

AB=DC [ABCD is ||gm] .......(i)
AB=EF [ABEF is a rectangle]....(ii)

from eqn 1 and 2
DC=EF

adding AB on both sides
AB+DC=AB+EF............(iii)

now AF<AD and BE<BC
BC+AD>AF+BE........(iv)

from eqn 3 and eqn 4

AB+CD+BC+AD>AB+EF+AF+BE

perimeter of ||gm>perimeter of rectangle

prooved!