The Cosmic Pool company is building a pool in Mary's back yard. The pool is to be 8ft longer than it is wide and cover 240 square feet of the back yard. Determine both dimensions of the pool and the perimeter

Answer:Part 1) The dimensions areLength is [tex]20\ ft[/tex], Width is [tex]12\ ft[/tex]Part 2) The perimeter is [tex]64\ ft[/tex]Step-by-step explanation:Part 1) Determine both dimensionsLetx-----> the length of the pooly----> the wide of the poolwe know thatThe area of the rectangle (pool) is equal to[tex]A=xy[/tex]we have[tex]A=240\ ft^{2}[/tex]so[tex]240=xy[/tex] -----> equation A[tex]x=y+8[/tex] ----> equation Bsubstitute equation B in equation A and solve for y[tex]240=(y+8)y[/tex][tex]240=y^{2}+8y[/tex][tex]y^{2}+8y-240=0[/tex]using a graphing tool to solve the quadratic equationthe solution is [tex]y=12\ ft[/tex]see the attached figureFind the value of x[tex]x=y+8[/tex] ------> [tex]x=12+8=20\ ft[/tex]Part 2) Find the perimeterThe perimeter of rectangle (pool) is equal to[tex]P=2(x+y)[/tex]we have[tex]x=20\ ft, y=12\ ft[/tex]substitute[tex]P=2(20+12)=64\ ft[/tex]