\a landscape architect has included a rectangular flower bed measuring 20 ft by 12 ft in her plans for a new building. she wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. if she has enough plants to cover 60 square feet for the border, how wide will the border be?

the width of the boundary will be equal to 1 ft

Explanation:

given,

size of rectangular flower bed = 20 ft × 12 ft

                                                  = 240 ft²

area of the boundary = 60 ft²

let width of the boundary be 'a'

Area of rectangular field = 60 ft² + (12 - 2 a) × (20 - 2 a )

240 ft² = 60 ft² + 240 -24 a - 40 a + 4 a²

4 a² - 64 a + 60 = 0

4 a² - 4 a - 60 a + 60 = 0

4 a( a - 1 ) - 60 (a -1) = 0

(4 a - 60 ) ( a - 1) =0

a = 1 , 15

we will accept the value of a = 1 and a = 15 is a vague result

so, the width of the boundary will be equal to 1 ft

a straight line sloped