Question 202753
Let x = the side of the smaller field, then (x+1) = the side of the middle field and (x+3) equal the side of the largest field.
The three areas, which sum to 38 sq.km. are:
{{{x^2+(x+1)^2+(x+3)^2  = 38}}} Simplify.
{{{x^2+(x^2+2x+1)+(x^2+6x+9) = 38}}}
{{{3x^2+8x+10 = 38}}} Subtract 38 from both sides.
{{{3x^2+8x-28 = 0}}} Factor this trinomial.
{{{(3x+14)(x-2) = 0}}} Apply the zero product rule.
{{{3x+14 = 0}}} or {{{x-2 = 0}}}
{{{3x = -14}}} or {{{x = 2}}} Discard the negative solution as the side must be a positive value.
{{{highlight(x = 2)}}}
The area of the smallest field is {{{x^2 = 4}}}sq.km.
The area of the middle field is {{{( x+1)^2 = 9}}}sq.km.
The area of the largest field is {{{(x+3)^2 = 25}}}sq.km.
{{{4+9+25 = 38}}}