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 fie
Algebra.Com
Question 280766: 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?
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
a^2+b^2+c^2=38
b=a+1
c=a+3
a = 2, b = 3, c = 5
field a 2^2=4
field b 3^3=9
field c 5^5=25
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Each field is square, so their areas are simply l*w = l^2 = w^2.
.
x = sides of square field 1
y = sides of square field 2
z = sides of square field 3
.
x^2 + y^2 + z^2 = 38 :: the sum of the areas of the three fields is 38
.
x = sides of the smallest field
y = x+1 = sides of the middle-sized field
z = x+3 = sides of the largest field
.
x^2 + (x+1)^2 + (x+3)^2 = 38
.
x^2 + (x^2 +2x +1) + (x^2 +6x +9) = 38
.
collecting terms and simplifying
.
3x^2 + 8x + 10 - 38 = 0
3x^2 + 8x -28 = 0
.
factoring
(3x +14 )(x - 2) = 0
.
The roots are x=-14/3 and x=2.
Negative values are the sides of fields are nonsensical, so we suspect x=2.
.
x = 2
y = x+1 = 3
z = x+3 = 5
.
Checking the proposed solution...
.
Does x^2 +y^2 +z^2 = 38?
2^2 = 4
3^2 = 9
5^2 = 25
4+9+25 = 38
YES!
.
Answer: The areas of each of the three square fields are: 4, 9, and 25.
.
Done
RELATED QUESTIONS
winter wheat: while finding the amount of seed needed to plant to plant his three square... (answered by Mathtut)
Winter wheat. While finding the amount of seed needed to plant his three square wheat... (answered by ankor@dixie-net.com)
Winter wheat. While finding the amount of seed needed to plant his three square wheat... (answered by stanbon)
Winter wheat. While finding the amount of seed needed
to plant his three square wheat... (answered by ankor@dixie-net.com)
Winter wheat. While finding the amount of seed needed
to plant his three square wheat... (answered by Earlsdon)
Winter wheat. While finding the amount of seed needed
to plant his three square wheat... (answered by Earlsdon)
Can you please help me with this problem?
Winter wheat. While finding the amount of... (answered by checkley77)
Winter wheat. While finding the amount of seed needed
to plant his three square wheat... (answered by stanbon)
Winter wheat. While finding the amount of seed needed to plant his three square wheat... (answered by gonzo)
92. Winter wheat. While finding the amount of seed needed to plant his three square... (answered by rcmcc)