Answer:
Part 1) [tex]A(x)=6x^{2} +3x-45[/tex]
Part 2) [tex]P(x)=10x+8[/tex]
Step-by-step explanation:
Let
L -----> the length of a rectangular playground
W ---> the width of a rectangular playground
we have
[tex]W=(2x-5)\ ft[/tex]
[tex]L=(3x+9)\ ft[/tex]
step 1
Find the area of the playground
The area of a rectangle is equal to
[tex]A=LW[/tex]
substitute the given values
[tex]A(x)=(3x+9)(2x-5)\\A(x)=6x^{2} -15x+18x-45\\A(x)=6x^{2} +3x-45[/tex]
step 2
Find the perimeter of the playground
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
substitute the given values
[tex]P(x)=2((3x+9)+(2x-5))[/tex]
[tex]P(x)=2(5x+4)[/tex]
[tex]P(x)=10x+8[/tex]
