pre calculus help :(

Question

Susan has a backyard in the shape of a square and the total area is 98 square metres. The backyard is laid out in four sections as shown in the diagram below. The patio has an area of 49 square metres. Calculate the exact perimeter of the flower bed as a radical. show work ! :) 

 

 Thank you so much!!

Answer 1

The total area of square shape backyard A =  98 m²

The area of patio Ap =  49 m²

Side of square shape backyard a = √A = √98 = √(2*7*7) = 7√2 m

Side of patio a_p= √Ap = √49 = √(7*7) = 7 m

Width of flower bed w = Side of square shape backyard - Side of patio = a - a_p = 7√2 - 7

Height of flower bed h = Side of patio = a_p = 7

The exact perimeter of the flower bed P = 2 ( Width of flower bed + Height of flower bed )

P = 2 (7√2 - 7 + 7 ) = 14√2

Solution : The exact perimeter of the flower bed is 14√2 m.