Flower garden and the grass border?

Around the outside of a rectangular flower bed 4 feet wide and 12 feet long, there is a grass border whose width is uniform and whose area is four times the area of the flower bed. Find the width of the border.
Flower garden and the grass border?
area(flower bed) = 4*12 = 48 sq.ft

area(grass border) = 4*48 = 192 sq.ft



let the width be x,



Total area(bed + border) = (12 + 2x) (4 + 2x)

192+48 = (12 + 2x) (4 + 2x)

240 = 48 + 24x + 8x + 4x^2

4x^2 + 32x + 48 = 240

divide by 4,

x^2 + 8x +12 = 60

x^2 + 8x - 48 = 0

(x + 12) (x - 4) = 0

x = -12 or x = 4

but x = -12 is not possible

so x = 4



Answer - Width of the border = 4 ft.



hope that helps.
Reply:Flower bed's dimensions are 4 * 12

Let x = width of border

So total thing has dimensions (4+2x) * (12+2x)



Total area must be 5 times area of flower bed

ie (4+2x) * (12+2x) = 5*4*12 = 240

4x^2 + 32x - 192 = 0

x = 4 feet