SOLUTION: 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 fielda

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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 fieldand that the side of the largest fieldwas 3 kilometers longerthan 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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