Question

The perimeter of the rectangle shown below is 23 feet. What is the missing side length. I have provided the answer choices and the image below.

Answer 1

We can pose the question in the following way (the sum of the sides is the perimeter). Since we have a rectangle, we have:

`2\cdot(4+(1)/(4)_{})+2n=23`

Then, we have to solve for n:

`8+(2)/(4)+2n=23\Rightarrow8+(1)/(2)+2n=23\Rightarrow2n=23-8-(1)/(2)`
`2n=15-(1)/(2)\Rightarrow2n=14+(1)/(2)\Rightarrow n=(14)/(2)+((1)/(2))/(2)\Rightarrow n=7+(1)/(4)\Rightarrow n=7(1)/(4)`

Then, n, the missing side length is 71/4 (option C).

We can check this result:

`8+(1)/(2)+2\cdot(7+(1)/(4)_{})=8+(1)/(2)+14+(1)/(2)=22+1=23`