Mason and Laney ran laps to train for the long-distance running team. The ratio of the number of laps Mason ran to the number of
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For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.
The dimensions are 475 m by 237.5 m.
_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.
The dimensions are 475 m by 237.5 m.
_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.
To solve this problem you must apply the proccedure shown below:
1- The formula for calculate the area of this rectangle is:
Where is the length and
is the heigth.
2. Let's call identify the heigth with the variable .
3. If the length is longer than the heigth, you have:
4. Therefore, you can write the following polynomial expression:
5. If you know the value of the heigth, you can susbstitute it into the polynomial expression shown above and you will obtain the area.
Therefore, the answer is: