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Sagot :
From the question
Perimeter of rectangular perian rug = 30ft
Area of rectangular persian rug = 54 ft square
We are to find length and width of the persian rug
let, length of pertianrug = l
width of persian rug = w
Recall perimeter P of a rectangle is given as
[tex]P=2(l+w)[/tex]Since perimeter = 30ft then
[tex]\begin{gathered} 30=2(l+w) \\ 15=l+w-------------1 \end{gathered}[/tex]Also, recall area A of a rectangle is given as
[tex]A=lw[/tex]But area = 54ft square then
[tex]54=lw------------2[/tex]Making l the subject in equation 2 we have
[tex]l=\frac{54}{w}--------------3[/tex]Substitite for l into equation 1, we have
[tex]\begin{gathered} 15=\frac{54}{w}+w \\ 15=\frac{54+w^2}{w} \\ 15w=54+w^2 \end{gathered}[/tex]This then gives
[tex]w^2-15w+54[/tex]By solving the quadraric equation we get
[tex]w=9,w=6[/tex]Net we are to solve for l
From equation 3
When w = 9
[tex]\begin{gathered} l=\frac{54}{9} \\ l=6 \end{gathered}[/tex]when w = 6
[tex]\begin{gathered} l=\frac{54}{6} \\ l=9 \end{gathered}[/tex]This implies that
l=6 when w = 9
l = 9 when w = 6
Finally
The length(longer side of the triangle is 9ft while
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