Question

A school wishes to form a rectangular playground using 160 meters of fencing. The playground borders the school building, so the fourth side does not need fencing. Find a function that gives the area of the playground in terms of x

Answer 1

Answer:

$A(x)=80x-\dfrac{x^2}{2}$

Step-by-step explanation:

Let the length of the school be x meters (this is also the length of playground) and the width of playground be y meters.

A school wishes to form a rectangular playground using 160 meters of fencing (two widths and one length must be fenced). So,

$x+2y=160\\ \\2y=160-x\\ \\y=80-\dfrac{x}{2}$

A function that gives the area of the playground in terms of x is

$A(x)=\text{Length}\times \text{Width}\\ \\A(x)=y\times x\\ \\A(x)=\left(80-\dfrac{x}{2}\right)\times x\\ \\A(x)=80x-\dfrac{x^2}{2}$