Question

Find the ratio of perimeters and areas of lands ABCD to ABFE. (Given AE = 2AD)

• A. Perimeter ratio = 1 ; Area ratio = 1/2
• B.
• C.
• D. Perimeter ratio = 1/2 ; Area ratio = 1

Answer 1

The correct option is C

Perimeter (ABCD) $=2(AB+AD)=2(x+y)$

Perimeter (ABFE) $=2(AB+AE)=2(x+2y)$ [Since, $AE=2AD$]

So, perimeter ratio $=\frac{\text{Perimeter}\left(ABCD\right)}{\text{Perimeter}\left(ABEF\right)}=\frac{2(x+y)}{2(x+2y)}=\frac{x+y}{(x+2y)}$

Area $\left(ABCD\right)=(AB\times AD)=xy$

Area $\left(ABFE\right)=$Area $\left(ABCD\right)$ [Both, $ABCD$ and $ABFE$ are lying on the same base and between the same parallel lines]

So, area ratio $=\frac{\text{Area}\left(ABCD\right)}{\text{Area}\left(ABEF\right)}=1$