How wide should the border be?

As part of a landscaping project, you put in a flower bed measuring 20 feet by 30 feet. To finish off the project, you are putting in a uniform border of pine bark around the outside of the rectangular garden. You have enough bark to cover 336 square feet. How wide should the border be?

How wide should the border be?
3 feet.

Assume the width of the border is x.

You have 100 linear feet (2*20+2*30) that has width = x, plus 4 corner squares each with dimensions x*x = x^2



4x^2 + 100x = 336

4(x^2 + 25x - 84) = 0

4(x-3)(x+28) = 0

x = 3 or -28, and we reject -28.
Reply:20ft by 30ft = 600 sq ft

adding a uniform area will result in an area of (20 + x)(30 + x)



Total area is 600 + 336 = 936



936 = (20 + x)(30 + x)



936 = 600 +50x + x^2



0 = x^2 +50x - 336



0 = (x - 6)(x + 56)



x = 6, -56



You cannot have a negative border, so the answer is a border of 6 ft to obtain a 26 by 36 area.
Reply:Use the perimeter of the flower bed (=20+20+30+30=100ft).



Divide the perimeter into the square footage of the bark you have available.



336/100 = 3.36 ft wide.
Reply:Maybe our Engineering graduate should go back to school.



Zaphod has the correct answer. Maybe we should check our work before we offer solutions.