Question

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

• A. Perimeter ratio = 1 ; Area ratio = $\frac{1}{2}$
• B. Perimeter ratio = $\frac{(x+y)}{2(x+2y)}$ ; Area ratio = $\frac{1}{2}$
• C. Perimeter ratio = $\frac{(x+y)}{(x+2y)}$ ; Area ratio = 1
• D. Perimeter ratio = $\frac{1}{2}$ ; Area ratio = 1

Answer 1

The correct option is C

Perimeter ratio = $\frac{(x+y)}{(x+2y)}$ ; Area ratio = 1

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

Perimeter (ABFE) = 2 (AB + AE) = 2 (x + 2y) (Since AE = 2AD)

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

Area (ABCD) = 2 (AB × AD) = 2xy

Area (ABFE) = Area (ABCD) [Both the parallelorgrams ABCD and ABFE are lying on the same base and between the same parallel lines]

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