Re: help
Hi, welcome to the forum!
Let's write out what we know.
$width = w + 5$
The length is also given, but it's been disguised a little bit.
The length of a rug is eight times greater then the width
This just translates to, $length = 8 \cdot width = 8 \cdot (w + 5)$.
Now we have everything we need from the question, let's look at the next part.
what is the ratio of the area of the rug to the perimeter of the rug in simplest form?
Let's focus first on finding the
area of the rug, and the
perimeter of the rug.
area of rug $= A = length \cdot width = 8(w + 5)(w + 5) = 8(w + 5)^2$.
perimeter of rug $= P = 2 \cdot length + 2 \cdot width = 2w + 10 + 16w + 80 = 18w + 90 = 18(w + 5)$.
Finally, the question asks for the ratio of the area to the perimeter. Let's call the ratio R.
Then, $R = A:P = \dfrac{A}{P} = \dfrac{8(w + 5)^2}{18(w + 5)^1}$
Can you finish it off? :)
