Question 161284
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?
:
Let x = side of the smallest field
:
Write an equation for each statement:
"the side of one field was 1 kilometer longer than the side of the smallest field"
(x+1) = side of this field
: 
" the side of the largest field was 3 kilometers longer than the side of the smallest field."
(x+3) = side of the longest field
:
" If the total area of the three fields is 38 square kilometers, then what is the area of each 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
Results:
3x^2 + 8x + 10 = 38
:
3x^2 + 8x + 10 - 38 = 0; subtract 38 from both sides
:
3x^2 + 8x - 28 = 0; our old friend the "quadratic equation" appears!
Factor this:
(3x + 14)(x - 2) = 0
The positive solution is all we want
x = +2 km is the side of he smallest 
then
2+1 = 3 km is the 2nd field
and
2+3 = 5 km is the largest field
:
:
Check solution, by finding the total area
2^2 + 3^ + 5^2 =
4 + 9 + 25 = 38