Two competitive neighbours build rectangular pools that cover the same area but are different shapes. Pool A has a width of (x + 3)m and a length that is 3m longer than its width. Pool B has a length that is double the width of Pool A. The width of Pool B is 4m shorter than its length. a. Find the exact dimensions of each pool if their areas are the same.b. Verify that the areas are the same.

Answer: a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m. b) Area of pool A is equal to area of pool B equal to 24.44 meters. Solution: Let’s first calculate area of pool A . Given that width of the pool A = (x+3)  Length of the pool A is 3 meter longer than its width. So length of pool A = (x+3) + 3 =(x + 6) Area of rectangle = length x width So area of pool A =(x+6) (x+3)        ------(1) Let’s calculate area of pool B Given that length of pool B is double of width of pool A. So length of pool B = 2(x+3) =(2x + 6) m Width of pool B is 4 meter shorter than its length, So width of pool B = (2x +6 ) – 4 = 2x + 2 Area of rectangle = length x width So area of pool B =(2x+6)(2x+2)        ------(2) Since area of pool A is equal to area of pool B, so from equation (1) and (2) (x+6) (x+3) =(2x+6) (2x+2)    On solving above equation for x    (x+6) (x+3) =2(x+3) (2x+2)   x+6 = 4x + 4    x-4x = 4 – 6 x = [tex]\frac{2}{3}[/tex] Dimension of pool A Length = x+6 = ([tex]\frac{2}{3}[/tex]) +6 = 6.667m Width = x +3 = ([tex]\frac{2}{3}[/tex]) +3 = 3.667m Dimension of pool B Length = 2x +6 = 2([tex]\frac{2}{3}[/tex]) + 6 = [tex]\frac{22}{3}[/tex] = 7.333m Width = 2x + 2 = 2([tex]\frac{2}{3}[/tex]) + 2 = [tex]\frac{10}{3}[/tex] = 3.333m Verifying the area:Area of pool A = ([tex]\frac{20}{3}[/tex]) x ([tex]\frac{11}{3}[/tex]) = [tex]\frac{220}{9}[/tex] = 24.44 meter Area of pool B = ([tex]\frac{22}{3}[/tex]) x ([tex]\frac{10}{3}[/tex]) = [tex]\frac{220}{9}[/tex] = 24.44 meter Summarizing the results: (a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m. (b)Area of pool A is equal to Area of pool B equal to 24.44 meters.