Question

In the given figure, a parallelogram ABCD and a rectangle ABEF are of equal area. Then,
(a) perimeter of ABCD = perimeter of ABEF
(b) perimeter of ABCD < perimeter of ABEF
(c) perimeter of ABCD > perimeter of ABEF
(d) perimeter of ABCD = $\frac{1}{2}$ perimeter of ABEF

Answer 1

We know, opposite sides of a rectangle are equal.
Therefore, in rectangle ABEF,
AB = EF ...(1)

Also, opposite sides of a parallelogram are equal.
Therefore, in parallelogram ABCD,
AB = DC ...(3)

From (1) and (3),
DC = EF
⇒ AB + EF = AB + DC ...(5)

Now, we know that, of all the line segments, perpendicular segment is the shortest.
∴ AF < AD
BE < BC
⇒ AF + BE < AD + BC ...(6)

Adding (5) and (6), we get
AB + EF + AF + BE < AB + DC + AD + BC
⇒ Perimeter of rectangle < perimeter of parallelogram

Hence, the correct option is (c).