Question

The area of a rectangular plot 30 feet long and 20 feet wide will be doubled by creating a border around the plot. What width should the border be to accomplish this?

Answer 1

5 feet

Explanation:

If you make a border `x` feet wide then the border along each length would be `30x` in area and there would be two of these. The boder along the width of the plot would be `20x` in area and again there would be two of these. You would also have four squares of border, one at each corner, that would be `x^2` in area.

The original area is `30xx20=600 feet^2`

So you have

`30x+30x+20x+20x+x^2+x^2+x^2+x^2=600`

`4x^2+100x=600`

`x^2+25x=150`

`x^2+25x-150=0`

`(x+30)(x-5)=0`

`x=-30 or x=5`

`x=5` as you cannot have a negative length.