Answer:
[tex]P=(19+50x)ft[/tex]
Step-by-step explanation:
A rectangle is a quadrilateral whose angles are all right angles. In this problem, we have a rectangle whose height [tex]h=9ft[/tex] and whose area is [tex]A=225xft^{2}[/tex]. We don't know the other side of the rectangle, but let's call it [tex]w[/tex]. So the area of a rectangle is:
[tex]A=h.w[/tex]
The perimeter is the distance around a shape in two dimensions. For our rectangle, our perimeter is:
[tex]P=2h+2w[/tex]
So our goal is to find [tex]w[/tex]. From the equation of the area:
[tex]w=\frac{A}{h} \\ \\ w=\frac{225x}{9}=25x[/tex]
If we substitute both this value and the height in the equation of the perimeter we get:
[tex]P=2(9+25x)ft \\ \\ \boxed{P=(19+50x)ft}[/tex]
