Question

HELP!

A rectangular plot of land has dimensions $x$ meters by $y$ meters. The plot of land is $216$ square meters in area. Farmer Ted encloses the rectangle with a fence and then divides the rectangle into two equal parts with another fence of length $x$ meters parallel to one of the sides. In terms of $x$ and $y,$ what is the total length of fence used? Describe the length of the fence used in terms of only one variable.

Answer 1

The length of the fence is $= 3x + \frac{ (432)}{x}$

A rectangular plot of land has dimensions $x$ meters by $y$ meters.

Total fence required

$= x + x + y + y + x \\= 3x+2y$

Area of the rectangular field

$x y = 216$  

⇒$\frac{216}{x} = y$  

substitute the value of $y$ in the equation $3x+2y$

$=3x + 2 \frac{ (216)}{x} \\= 3x + \frac{ (432)}{x}$

The length of the fence is $= 3x + \frac{ (432)}{x}$

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