Answer:
[tex]A(x)=80x-\dfrac{x^2}{2}[/tex]
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,
[tex]x+2y=160\\ \\2y=160-x\\ \\y=80-\dfrac{x}{2}[/tex]
A function that gives the area of the playground in terms of x is
[tex]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}[/tex]
The area of a shape is the amount of space it occupies.
The function of area is: [tex]\mathbf{A(x) = x(160 -2x)}[/tex]
The perimeter is given as:
[tex]\mathbf{P = 160}[/tex]
Because one of the sides does not need fencing, the perimeter would be:
[tex]\mathbf{P = 2x + y}[/tex]
Make y the subject
[tex]\mathbf{y = P - 2x}[/tex]
Substitute 160 for P
[tex]\mathbf{y = 160 - 2x}[/tex]
The area of a rectangular fence is:
[tex]\mathbf{A = xy}[/tex]
Substitute [tex]\mathbf{y = 160 - 2x}[/tex]
[tex]\mathbf{A = x(160 -2x)}[/tex]
Express as a function
[tex]\mathbf{A(x) = x(160 -2x)}[/tex]
Hence, the function of area is: [tex]\mathbf{A(x) = x(160 -2x)}[/tex]
Read more about areas at:
https://brainly.com/question/11957651
