Question 124227
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