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:

$2\cdot(4+\frac{1}{4}_{})+2n=23$

Then, we have to solve for n:

$8+\frac{2}{4}+2n=23\Rightarrow8+\frac{1}{2}+2n=23\Rightarrow2n=23-8-\frac{1}{2}$$2n=15-\frac{1}{2}\Rightarrow2n=14+\frac{1}{2}\Rightarrow n=\frac{14}{2}+\frac{\frac{1}{2}}{2}\Rightarrow n=7+\frac{1}{4}\Rightarrow n=7\frac{1}{4}$

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

We can check this result:

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