Need help with Word Problem

[Guest]

Winter wheat. While finding the amount of seed needed to plant his 3 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?

Please help with this problem. I do not know how to set this one up.

 

[soroban]

Hello, birdbook!

While finding the amount of seed needed to plant his 3 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?

As I've asked so often: did you make a sketch?

                                        * - - - - *
                      * - - - *         |         |
      * - - *         |       |         |         |
      |     |         |       |x+1      |         |x+3
      |     |x        |       |         |         |
      |     |         |       |         |         |
      * - - *         * - - - *         * - - - - *
         x               x+1                x+3

The areas of the three square fields are: \(\displaystyle \,x^2,\;(x+1)^2,\;(x+3)^2\)

And we're told that the total area id 38 kn².

There is our equation! . . . \(\displaystyle \,x^2\,+\,(x+1)^2\,+\,(x+3)^2\;=\;38\)

Got it?