plot of land

[miamivince]

A plot of land has frontage 88 meters and sides lengths of 35 and 88 meters. If it is divided into 2 lots of equal area by a straight fence parallel to both sides, how far from the frontage should the fence be located ? The soln given is 33 meters.
I drew a rectangle which shares common 88 meter length with a righr angle triangle drawn above the rectangle . The area of the rectangle is 88 * 35 . 44 . The area of the tri is 44 * 82 , summed , gives a combined 6,600 m ^ 2.
Am I close ? Thanks. Will the 2 new plots be a 2 quads ? I have seen easier questions ON A SIMILAR TOPIC.

 

[HallsofIvy]

A plot of land has frontage 88 meters and sides lengths of 35 and 88 meters. If it is divided into 2 lots of equal area by a straight fence parallel to both sides, how far from the frontage should the fence be located ? The soln given is 33 meters.
I drew a rectangle which shares common 88 meter length with a righr angle triangle drawn above the rectangle . The area of the rectangle is 88 * 35 . 44 . The area of the tri is 44 * 82 , summed , gives a combined 6,600 m ^ 2.
Am I close ? Thanks. Will the 2 new plots be a 2 quads ? I have seen easier questions ON A SIMILAR TOPIC.

I'm not clear what you mean by "side lengths of 35 and 88 m". Are those sided that attach to the frontage? But then what is the length of the fourth side? Or are you talking about a triangular plot? If so, then what "rectangle" are you referring to?

 

[soroban]

Hello, miamivince!

I assume there is a diagram somewhere.
Could you describe it more accurately?
As stated, the problem is quite silly.

A plot of land has frontage 88 meters and sides lengths of 35 and 88 meters.
If it is divided into 2 lots of equal area by a straight fence parallel to both sides,
how far from the frontage should the fence be located?
The sol'n given is 33 meters.

You made no references to right angles, so the plot could look like this:

                               o
                          *   *
                     *       *
                *           *
           *               *
      o                   * 88
       *                 *
        *               *
      33 *             *
          o  *  *  *  o
                 88

Assuming the "sides" are perpendicular to the "frontage",
. . the diagram would look like this:

                  o
               *  *
            *     *
         *        *
      o           * 88
      *           *
   33 *           *
      *           *
      o  *  *  *  o
           88

A divider is placed parallel to both sides.
Then the diagram looks like this:

                  o
               *  *
            *|    *
         *   |    *
      o      |    * 88
      *      |    *
   33 *      |    *
      *      |    *
      o  *  *  *  o
           88

"How far from the frontage should the fence be located?"

Since the fence touches the frontage,
. . the distance is 0 meters.


I have a theory:
. . the fence is perpendicular to the sides.