Stephon has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.Let x represent the length of one side of the square patio. Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 20 feet by 20 feet.

Answer:  The expressions for the length and width of the new patio are[tex]\ell=x+4,~~w=x-4.[/tex]And the area of the new patio is 384 sq. feet.Step-by-step explanation:  Given that Stephen has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.The length of one side of the square patio is represented by x.We are to write the expressions for the length and width of the new patio and then to find the area of the new patio if the original patio measures 20 feet by 20 feet.Since Stephen wants to reduce width of the patio by 4 feet, so the width of the new patio will be[tex]w=(x-4)~\textup{feet}.[/tex]The length of the patio is increased by 4 feet, so the length of the new patio will be[tex]\ell=(x+4)~\textup{feet}.[/tex]Now, if the original patio measures 20 feet by 20 feet, then we must have[tex]w=x-4=20-4=16~\textup{feet}[/tex]and[tex]\ell=x+4=20+4=24~\textup{feet}.[/tex]Therefore, the area of the new patio is given by[tex]A_n=\ell \times w=24\times16=384~\textup{sq. feet}.[/tex]Thus, the expressions for the length and width of the new patio are[tex]\ell=x+4,~~w=x-4.[/tex]And the area of the new patio is 384 sq. feet.