Question

Find the dimensions of a rectangular Persian rug whose perimeter is 30 ft and whose area is 54 ft(to the second power) The Persian rug has a length (longer side) of__ft and a width (shorter side) of__ft ?

Answer 1

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

`P=2(l+w)`

Since perimeter = 30ft then

`\begin{gathered} 30=2(l+w) \\ 15=l+w-------------1 \end{gathered}`

Also, recall area A of a rectangle is given as

`A=lw`

But area = 54ft square then

`54=lw------------2`

Making l the subject in equation 2 we have

`l=(54)/(w)--------------3`

Substitite for l into equation 1, we have

`\begin{gathered} 15=(54)/(w)+w \\ 15=(54+w^2)/(w) \\ 15w=54+w^2 \end{gathered}`

This then gives

`w^2-15w+54`

By solving the quadraric equation we get

`w=9,w=6`

Net we are to solve for l

From equation 3

When w = 9

`\begin{gathered} l=(54)/(9) \\ l=6 \end{gathered}`

when w = 6

`\begin{gathered} l=(54)/(6) \\ l=9 \end{gathered}`

This implies that

l=6 when w = 9

l = 9 when w = 6

Finally

The length(longer side of the triangle is 9ft while