In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7m and 12m. The area of the pool is 36 sq. m. (a) Based on the information given above, form a quadratic equation in terms of x. (b) Find the width of the sidewalk around the pool.

 

Case Study – 04

In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7m and 12m. The area of the pool is 36 sq. m.

(a)          Based on the information given above, form a quadratic equation in terms of x.

(b)         Find the width of the sidewalk around the pool.

Soln:

Given that Outside Edges of side walk

          L = 12m

          B = 7 m

          Area of the Pool = 36 cm²

          Width of the side walk = x m

(a)          Based on the information given above, form a quadratic equation in terms of x.

Inner length of the pool = (12 – 2x) m

Inner breadth of the pool = (7 – 2x) m

Area of the pool = Length x breadth

          36 m          =  (12 – 2x) (7 – 2x)

          36  = 84 – 24x + 4x² – 14x

          36 = 84 – 38x + 4x²

i.e.,    4x² – 38x + 84 – 36 = 0

The required quadratic equation is

           4x² – 38x + 48 = 0

(b)         Find the width of the sidewalk around the pool

Solve the above quadratic equation

              4x² – 38x + 48 = 0

              2x² – 19x + 24 = 0

              2x² – 16x – 3x + 24 = 0

              2x (x – 8) -3(x – 8) = 0

              (2x – 3) (x – 8) = 0

     i.e.,    (2x – 3) = 0 or (x – 8) = 0

     i.e.,    x = 3/2 or

              x = 8

     Width of the side walk 8m is not possible

     Therefore, width of side walk = 3/2 m