Question 205134This question is from textbook Elementary and Intermediate Algebra
: 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?
This question is from textbook Elementary and Intermediate Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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
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