How do I solve?

Question

A person has a rectangle garden with a width of 6ft and a length of 10 ft. To form a border of equal width, they plan to place concrete around the outside of the garden. If they have just enough concrete to cover 80 square feet of land, find the largest width of the border they can make.

Answer 1

Consider the border as made up of 4 rectangles. Along the narrow side, the two both have a length of 6 and width of b. Along the long side, each has a length of 10 + 2b and a width of b. So, the total maximum area of 80 is also:

2(6b) + 2(b(10+2b)) = 80 => 12b+20b+4b²=80 => 4b²+32b-80=0 which can then be solved via the quadratic formula