Stacy wants to build a patio with a small, circular pond in her backyard.The pond will have a 6-foot radius. She also wants to install tiles in the remaining area of the patio. The length of the patio is 13 feet longer than the width.If the cost of installing tiles is $1 per square foot, and the cost of installing the pond is $0.62 per square foot, then which of the following inequalities can be used to solve for the width, x, of the patio, if Stacy can spend no more than $536 on this project?

we know that

step 1
the area to install tiles is equal to A
A=area rectangle-area of a circle

area of a rectangle=(13+x)*x-----> (13x+x²) ft²

area of a circle=pi*r²-----> pi*6²------> 36*pi ft²
A=(x²+13x)-36*pi  ft²

step 2
find the cost of installing tiles CT
CT=$1*[(x²+13x)-36*pi]-----> CT=$x²+$13x-$36*pi

step 3
find the cost the of installing the pond CP
CP=$0.62*36*pi------> CP$22.32*pi

step 4
find the inequality
we know that
CT+CP [tex] \leq [/tex] $536
[$x²+$13x-$36*pi]+[$22.32*pi]  [tex] \leq [/tex] $536

[$x²+$13x-$13.68*pi]  [tex] \leq [/tex] $536

the answer is the option D