Question

\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?

Answer 1

the width of the boundary will be equal to 1 ft

Step-by-step 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