Word Problem

Question

At a tennis club, a 13,500ft squared rectangular area is partitioned into three rectangular courts of equal size. A total of 740 feet of fencing is used to enclose the three courts, including the interior sides. 

 

(answer will be): __ft by __ft

Answer 1

Let's say Width is W and the other side is L

 

If you divide the area in three rectangles of the same size, you can draw 2 interior lines parallel to W.

 

 

What you know is:  W x L = 13500  (The area of the original triangle)

 

Now the fence is on the lines. So you have 4 horizontal lines W. And you have still 2 vertical lines L

 

=>

 

4 W + 2 L = 740  (four lines of horizontal fences + 2 lines of vertical fences)

 

=>

 

2 L = 740 - 4 W

 

L = 370 - 2W,     replacing this in W x L = 13500 (first equation)

 

W x (370 - 2W) = 13500

 

370W - 2 W² = 13500

 

2W² - 370W + 13500 = 0

 

Solving with quadratic equation  X =      -b +/- √(b2 - 4ac)
                                                           _______________
                                                                      2a   

 

We have two possible values

 

W₁= 135   or    W₂= 50    =>    L1= 100   or    L2= 270

 

 

So you have two possible fields of 13500ft area one of them is 135ft by 100ft

 

and the other one is 50ft by 270ft

 

 

Both can be divided in three equal parts, both are going to have area of 13500ft², and both are going to have 740 feet of fence.