SOLUTION: Can you please help? I am stuck on a problems this evening and am getting no where. The one problem I would like to ask is: There are 3 square wheat fields. A man observed that

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Question 190793: Can you please help? I am stuck on a problems this evening and am getting no where.
The one problem I would like to ask is:
There are 3 square wheat fields. A man observed that the side of one field was 1 kilometer longer than the side of the smallest field and the side of the largest field was 3 kilometers longer than the side of the smallest field. The total area of the 3 fields is 38 square kilometers. I am suppose to find the area of each field.
I have tried setting up with x+(x+1)+(x+2)=38 or x^2+3x+3x+9
Am I on the right track in finding the correct answer? Please help.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
There are 3 square wheat fields. A man observed that the side of one field was 1 kilometer longer than the side of the smallest field and the side of the largest field was 3 kilometers longer than the side of the smallest field. The total area of the 3 fields is 38 square kilometers. I am suppose to find the area of each field.
I have tried setting up with x+(x+1)+(x+2)=38 or x^2+3x+3x+9
---------------
x^2 is the smallest
(x+1)^2 is another
(x+3)^2 is largest
Add them up

(3x+14)*(x-2) = 0
x = 2
Area = 4, 9 and 25

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

That would be no and no, refering to your two attempts.

Let x represent the measure of the side of the smallest square.

Then x + 1 must represent the measure of the side of the middle-sized square, and x + 3 must represent the measure of the side of the largest square.

The area of the smallest square:

The area of the middle-sized square:

The area of the largest square:

And the sum of these areas is

So:

Expand the binomials:

Collect terms:

You should be able to take it from here. This thing is ugly, but it does factor, but you might just want to use the quadratic formula instead of messing around trying to find the factors. You will get two roots one of which will be negative. Exclude that root because you are trying to find the measure of something. The positive root will be the length of the side of the smallest square.

John