a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .
let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50 w – 54 = 0 ⇒ 2 w 2 + 25 w – 27 = 0 ⇒ ( w – 2 ) ( w + 27 ) = 0 thus w = 2 or – 27 ∴ with of the path = 2 m answer c
subtract(sqrt(add(54, power(divide(rectangle_perimeter(15, 10), const_4), const_2))), divide(rectangle_perimeter(15, 10), const_4))