Question

If parallelogram ABCD and rectangle ABEM are of equal area, then:

• A. Perimeter of AMEB = Perimeter of ADCB
• B. Perimeter of AMEB $<$ Perimeter of ADCB
• C. Perimeter of AMEB $>$Perimeter of ADCB
• D. Perimeter of AMEB = $\frac{1}{2}$ Perimeter of ADCB

Answer 1

The correct option is B

Perimeter of AMEB $<$ Perimeter of ADCB

In right angled $\Delta AMD$
$A{D}^2$ = $A{M}^2$ + $M{D}^2$ (by Pythagoras theorem)
$\Rightarrow AD>AM$
Similarly, In right angled $\Delta BEC$
$B{C}^2$ = $B{E}^2$ + $E{C}^2$
$\Rightarrow BC>BE$
AB = DC = ME (opposite sides of rectangle and parallelogram)
Perimeter of rectangle = AM + ME + EB + AB.
Perimeter of parallelogram = AB + BC + DC + AD.
Hence Perimeter of ADCB $>$ Perimeter of AMEB.