A rectangular plot of lawn of length and width respectively x and y metres is surrounded by a
pathway of 2 metres width. The total area of pathway is :

(A) 2x + 2y + 4

(B) 2x + 2y + 8

(C) 4x + 4y + 8

(D) 4x + 4y + 16

• D) 4x + 4y + 16
  
  Area of pathway = (area of rectangle of pathway + lawn ) - ( area of lawn )
  
  Length and width of outer rectangle = (x + 4) , (y + 4)
  Length and width of inner rectangle = x , y
  
  => area of pathway = (x + 4)(y + 4) - xy
  = 4x + 4y + 16
• 12 years agoHelpfull: Yes(52) No(0)
• (x+4)(y+4)-xy= 4x+4y+16
• 12 years agoHelpfull: Yes(6) No(0)
• (A)2x+2y+4
  area of the pathway=(x+2)*(y+2)-x*y
  x*y+2x+2y+4-x*y
  2x+2x+4
• 12 years agoHelpfull: Yes(3) No(10)
• the total area of pathway is: ((x+4)(y+4)-(x*y))=4x+4y+16
• 12 years agoHelpfull: Yes(2) No(0)
• 1st time area of rect = xy
  2nd time area of rect = (x+2+2)(y+2+2)=(x+4)(y+4)
  =4x+4y+xy+16
  
  area of pathway = total inc area - old area
  = (4x+4y+xy+16) - xy
  =4x+4y+16
  
• 11 years agoHelpfull: Yes(2) No(0)
• How come x+4? pathway width is only 2mts na?
• 10 years agoHelpfull: Yes(2) No(0)
• correct ans. is D
  cause area of pathway=area of lawn+pathway-area of lawn=(x+4)*(y+4)-x*y=4x+4y+16
• 12 years agoHelpfull: Yes(1) No(0)
• how become Length and width of outer rectangle = (x + 4) , (y + 4)?
• 10 years agoHelpfull: Yes(1) No(0)
• Total area=path area +rect area=(x+4)*(y+4);
  path area= total area- rect area;
  hence D
  
• 8 years agoHelpfull: Yes(0) No(0)