Question 885582: Question 4: (1 point)
At a tennis club, a 15,000 ft2 rectangular area is partitioned into three rectangular courts of equal size. A total of 800 feet of fencing is used to enclose the three courts, including the interior sides.
Maple plot
What are the possible dimensions, in feet, of the entire rectangular area?
Select all that apply.
(a)
25feet by 600feet
(b)
100feet by 150feet
(c)
100feet by 300feet
(d)
300feet by 50feet
(e)
100feet by 50feet
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The answer they want is  .
I would answer that and try hard not to say more.
Answer (b) Is also mathematically correct, and looks like a possibility for people not familiar with tennis.
That makes the question culturally biased, and makes the designer of the question look incompetent at math.
However, pointing out that may not gain you any points.
MULTIPLE CHOICE STRATEGY:
Think efficiently, and do not waste time thinking too much and/or writing too many equations.
You can use the area information to quickly rule out (c) and (e):
The area for (c) is   , and
the area for (e) is  .
Neither one of those is  , so (c) and (e) are not solutions.
"Make plot" means draw a quick sketch.
It does not need to be a good drawing, and it cannot be to scale since you do not know the answer yet.
The red lines represent the   of fencing, so
 --->
How do choices (a), (b), and (d), fare against that requirement?
For (a)  , so (a) does not work.
You did not even need to calculate because  length is by itself more than  .
For (d)  , so is a solution.
Since the problem is worth just one point, you do not need to think too long about it.
If all the choices are single answers,
as soon as you get an answer that everyone would like,
even if you have not tried the other options,
you choose that answer, and move on to another question.
THINKING TOO MUCH:
For (b)  , does not work.
However,  works, so (b) 100feet by 150feet could be a solution, if  and  .
In the plot/sketch,  and  were just variable names representing the measurements of the two sides of the big rectangle.
It is not necessary that  , or that meant the longer side of that rectangular area.
I bet the people who designed the question never thought of that.
Answer (b) 100feet by 150feet is mathematically correct.
Unfortunately, and would mean that each court would be   by  , and that is too narrow and too long for a tennis court. (I looked it up).
WRITING TOO MANY EQUATIONS:
 = one of the dimensions of the total area to be fenced, in feet.
 = the other dimension of the total area to be fenced, in feet.
 <---> (because the area is 15,000 square feet).
 <---> (because 800ft is total amount of fence, and the sketch/plot shows that  is that length as a function of and ).
 ---> ---> ---> --->
Any way you solve that equation, you get two solutions:
either  --> ---> ,
or  --> ---> .
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