Question

The given figure shows a parallelogram ABCD. E is a point in AD and CE produced meets BA produced at point F. If $AE=4cm,AF=8$ cm and AB $=12$ cm. find the perimeter of the parallelogram ABCD.

• A. $42$ cm
• B. $44$ cm
• C. $46$ cm
• D. $48$ cm
• E. $40$ cm
  
• F. $38$ cm
  
• G. $36$ cm

Answer 1

The correct option is B $44$ cm

In $△AFE$ and $△BFC$,
$\angle AFE=\angle BFC$ (Common angle)
$\angle AEF=\angle BCF$ (Corresponding angles of parallel lines)
$\angle FAE=\angle CBF$ (Corresponding angles of parallel lines)
Thus, $△AFE\sim △CFB$ ($AAA$ rule)
Hence, $\frac{AF}{BF}=\frac{AE}{BC}$
$\frac{AF}{AF+AB}=\frac{AE}{BC}$
$\frac{8}{8+12}=\frac{4}{BC}$
$BC=\frac{4\times 20}{8}$
$BC=10$ cm
Perimeter of parallelogram = $AB+BC+BC+AD$
Perimeter of parallelogram = $2(AB+BC)$
Perimeter of parallelogram = $2(12+10)$ (Opposite sides are equal)
Perimeter of parallelogram = $44$ cm