Question 124227: Hello Tutors,
can you help me please with the problem?.
Winter wheat. while finding the amount of of seed needed to plans his tree square wheat fields, Hank observed that the side of one fields was 1 kilometers longer than the side of the smallest field and that the side of the largest fields was 3 kilometers longer than the side of the smallest field.. If the trotal area of the three field is 38 square kilometers, then what is the area of each field?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three square fields
:
Hank observed that the side of one field was 1 kilometers 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 field is 38 square kilometers, then what is the area of each field?
:
Let x = side of the smallest field
:
It said 1 field was 1km longer than the smallest field, therefore
(x+1) = side of the medium field
:
It said one side of the largest field was 3 km longer than the smallest, therefore:
(x+3) = side of the largest field
:
It said the total area = 38 sq/km, therefore:
:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
Group like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
Combine like terms
3x^2 + 8x - 28 = 0; our old friend, the quadratic equation
Factors to:
(3x + 14)(x - 2) = 0
:
x = + 2 km side of the smallest field (it's the positive solution we want here)
then
3 km is the side of the medium field
and
5 km is the side of the larger field
:
Check solution by finding the area of each
2^2 + 3^2 + 5^2 =
4 + 9 + 25 = 38
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