While finding the amount of seed needed to plant his three s

While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?

Solution

let x = side of the smallest field
then
(x+1) = side of the middle sized field
and
(x+3) = side of the largest field
:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
Combine like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 = 38
:
3x^2 + 8x + 10 - 38 = 0
:
3x^2 + 8x - 28 = 0
Factor this to
(3x + 14)(x - 2) = 0
Positive solution
x = 2 km, 2^2 = 4 sq/km, area of the smallest field
and
2 + 1 = 3 km; 3^2 = 9 sq/km; the middle field
and
2 + 3 = 5 km; 5^2 = 25 sq/km; the largest field
:
:
Check solution:
4 + 9 + 25 = 38