Question

A rectangle and a parallelogram of equal area and equal base are given. If r and p denote their respective perimeters, then

(a) r = p 

(b) r = 2p 

(c) r > 2p 

(d) r < p

Answer 1

(d) r < p

Perimeter of the rectangle ABCD = 2 (AB + AD) + (DC + CB)    … (i) 

Perimeter of parallelogram ABFE = 2 (AB + AE ) + (EF + FB)    … (ii)

In right angled ΔADE, AE is the hypotenuse and the hypotenuse being the longest side in a Δ,

AE > AD ⇒ BF > BC 

Also, AB = DC and AB = EF ⇒ DC = EF.

∴ From (i) and (ii) 

Perimeter of rectangle < Perimeter of parallelogram.