Let the width of the path = W m
then, length of plot with path = (15 + 2W) m
and breadth of plot with path = (10 + 2 W) m
Therefore, Area of rectangular plot (without path)
= 15 × 10 = 150 m2
and Area of rectangular plot (with path)
= 150 + 54 = 204 m2
Hence, (15 + 2W) × (10 + 2W) = 204
⇒ 4W2 + 50 W – 54 = 0
⇒ 2W2 + 25 W – 27 = 0
⇒ (W – 2) (W + 27) = 0
Thus W = 2 or –27
with of the path = 2 m