Question 220981
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?
:
I understand x^2 , x+1, x+3, however, when I write the equation to separate I cannot get to area of each field if total is 38.
:
I think it should be:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
Combine like terms
3x^2 + 8x + 10 = 38
:
3x^2 + 8x + 10 - 38 = 0
:
3x^2 + 8x - 28 = 0
Factors to
(3x + 14)(x - 2) = 0
Positive solution
x = 2 km
;
The three field sides, 2, 3, 5
;
Check:
2^2 + 3^2 + 5^2 = 38