SOLUTION: Winter wheat. 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 th
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-> SOLUTION: Winter wheat. 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 th
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Question 200549This question is from textbook Elementary and Intermediate Algebra
: Winter wheat. 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
You can put this solution on YOUR website! Hank observed that:
the side of one field was 1 kilometer longer than the side of the smallest field
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?
:
The sides of the 3 fields
x = smallest field side
(x+1) = medium field side
(x+3) = largest field side
:
Area equation:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
remove brackets, combine like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
Results in a quadratic equation
3x^2 + 8x - 28 = 0
Factors to:
(3x + 14)(x - 2) = 0
Positive solution:
x = 2 km is the side of the small field
Area: 2^2 = 4 sq/km
then
2 + 1 = 3 km is the side of the medium field
Area: 3^2 = 9 sq/km
and
2 + 3 = 5 km is the side of the large field
Area: 5^2 = 25 sq/km
;
;
Check solution: 4 + 9 + 25 = 38
