Question

The ratio of the dimensions of a rectangular patio are 4:7. if the shorter

dimension is 10 feet, What are the area and perimeter of the patio?

Answer 1

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:

`(4)/(7) =(10)/(x)`

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.

`(4)/(7)*(2.5)/(2.5)=(10)/(17.5)`

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`

So we can plug our dimensions into the formula:
`10*17.5=175`

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 175 square feet.

PERIMETER

The formula for the perimeter of a rectangle is:
`2(w+l)`

We can plug our dimensions into the formula:
`2(10+17.5)=55`

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 55 feet.