If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:
![\frac{4}{7} =\frac{10}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B7%7D%20%3D%5Cfrac%7B10%7D%7Bx%7D)
You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.
![\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B7%7D%2A%5Cfrac%7B2.5%7D%7B2.5%7D%3D%5Cfrac%7B10%7D%7B17.5%7D)
This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is: ![w*l](https://tex.z-dn.net/?f=w%2Al)
So we can plug our dimensions into the formula: ![10*17.5=175](https://tex.z-dn.net/?f=10%2A17.5%3D175)
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.
PERIMETER
The formula for the perimeter of a rectangle is: ![2(w+l)](https://tex.z-dn.net/?f=2%28w%2Bl%29)
We can plug our dimensions into the formula: ![2(10+17.5)=55](https://tex.z-dn.net/?f=2%2810%2B17.5%29%3D55)
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.