Answer:
[tex]15x^2+380x+2400[/tex]
The diagram is shown below for reference.
Step-by-step explanation:
We are given the length and width of old pumpkin patch as [tex]60[/tex] meters and [tex]40[/tex] meters respectively.
It further says length is increased by [tex]5x[/tex] meters and width increased by [tex]5x[/tex] meters.
So the length of the new pumpkin patch would be [tex]60+5x[/tex] meters.
And the width would be [tex]40+3x[/tex] meters.
We know area of a rectangular shape [tex]=length \times width[/tex]
So, plugging the above values, we get the area of the new pumpkin patch as:
[tex]=(60+5x)\times (40+3x)\\=2400+180x+200x+15x^2\\=2400+380x+15x^2\\=15x^2+380x+2400[/tex] on rearranging.
Thus the function of the area of the new pumpkin patch would be:
[tex]f(x) = 15x^2+380x+2400[/tex]
