SOLUTION: Hank has three square fields. One field is 1 kilometer longer than the side of the smallest field. The side of the largest field is 3 kilometers longer than the smallest field. The

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Question 151761: Hank has three square fields. One field is 1 kilometer longer than the side of the smallest field. The side of the largest field is 3 kilometers longer than the smallest field. The total area of the fields is 38 square kilometers . What is the area of each field? This doesn't sound like it should be difficult but I can't figure it out. A=S^2 ???? 38= S^2 + S^2+1^2 + S^2 +3^2 ???
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
It can get confusing.
First name the sides of the fields.
How about S for small field, L for large field, and M for the middle field.
Since they're squares the area of each field is,

The largest field side is 3 km larger than the small field.

One field is 1 kilometer longer than the side of the smallest field.
I'm assuming this is the middle field.

The total area is 38 km^2.

Now substitute for M and L.

Note the expansion of the squares.
Check on the FOIL method if this isn't clear.

You can factor this quadratic equation.

Two solutions:

A negative length does not make sense in this case so we throw out that answer.

Then from above,

and finally

The smallest field is 4 km^2, the middle field is 9 km^2, and the large field is 25 km^2.