If parallelogram ABCD and rectangle ABEM
are of equal area, then
M D E C
A B
(1) Perimeter of ABCD = perimeter of ABEM
(2) Perimeter of ABCD < perimeter of ABEM
(3) Perimeter of ABCD > perimeter of ABEM
(4) Perimeter of ABCD =
1
2 perimeter of ABEM
Answers
in parallelogram ABCD , ab is equal to cd and ac is equal to bd and in same the rectangle ABEM ab is equal to em and also am is equal to be
Answer: option (3)
Step-by-step 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)
Since the perpendicular distance between two parallel sides of a parallelogram is always less than the length of the other parallel sides.
BE < BC and AM < AD
[In a right angled triangle, the hypotenuse is always greater than the other side]
On adding both above mentioned, we get,
BC + AD> BE + AM
On adding AB + CD both sides, we get
AB + CD + BC + AD> AB + CD + BE + AM
⇒ AB+BC + CD + AD> AB+BE + EM [∴ CD = AB = EM] + AM
Perimeter of parallelogram ABCD > perimeter of rectangle ABEM