Answer:
[tex]D=(20.42)(28.42)[/tex]
Step-by-step explanation:
From the question we are told that
Width [tex]W=24ft[/tex]
Length [tex]L=32ft[/tex]
She can afford to buy 560 square feet of carpeting
Let
[tex]S=width\ of\ strip[/tex]
Generally the Dimension of the rug is mathematically given as
Width of Rug [tex]W' = (24- 2S)ft[/tex]
Length of Rug [tex]L'= (32-2S) ft[/tex]
Generally the width of strip S is mathematically given by
[tex](32-2s)*(24-2s)=560[/tex]
[tex]-4s-112s+208=0[/tex]
[tex]s_1=-29.7\\s_2=1.748[/tex]
Therefore the width is
[tex]s=1.748[/tex]
Generally the dimension of the rug D is mathematically given as
Width of Rug [tex]W' = (24- 2s)ft[/tex]
[tex]W' = (24- 2(1.79))ft[/tex]
[tex]W' =20.42ft[/tex]
Length of Rug [tex]L'= (32-2S) ft[/tex]
[tex]L'= (32-2(1.79)) ft[/tex]
[tex]L'=28.42 ft[/tex]
Therefore dimension of Rug is given by
[tex]D=(20.42)(28.42)[/tex]
