Try the following problems

Question

<!--[if !supportLists]-->1.                  <!--[endif]-->A rectangular garden has a length of 3x – 2 m and a width of 2x + 3 m.       There is a uniform concrete walk x + 1 m wide around it.

 

<!--[if !supportLists]-->a.       <!--[endif]-->      Find the perimeter along the edge of the concrete walk in terms of x.

 

<!--[if !supportLists]-->b.      <!--[endif]-->       Find the area of the concrete walk in terms of x.

 

Answer 1

length of garden = 3x-2

breadth of garden = 2x+3

width of concrete walk = x+1

So the length of garden along with width of concrete walk = 3x-2 + 2* (x+1) = 3x-2 +2x +2 = 5x

and the breadth of garden along with width of concrete walk = 2x +3 + 2*(x+1) = 2x +3 + 2x +1 = 4x +4

Area of garden without concrete walk = (3x-2)(3x+3) = 9x² +3x -6

Area of garden with concrete walk = 5x * (4x +4) = 20x² + 20x

a) The perimeter along the edge of the concrete walk = 2{(5x) + (4x +4)} = 18x + 8

b) The area of the concrete walk = Area of garden along with concrete walk - Area of garden without concrete walk = (20x² + 20x) - 9x² +3x -6 = 11x² +23x -6