Question

Suppose a square has a side length given by the expression $\frac{x+5}{8x}$. What is the perimeter of the square?

F $\frac{4x+20}{5x}$

G$\frac{2x+10}{x}$

H$\frac{x+5}{4x}$

J$\frac{x+5}{2x}$

Short answer

Option J is the correct answer.

Step-by-step solution

Step 1. Define a square.

The square is a quadrilateral having all the sides equal and the measure of all the angles to be $90°$.

Step 2. Define the perimeter of the square.

The perimeter of the square is equal to 4 times the length of the side of the square.

Perimeter of the square$=4$ (length of the side of the square) ……….. (1)

Step 3. Determine the perimeter of the given square.

The length of the side of the square$=\frac{x+5}{8x}$

Use equation to determine the perimeter of the square.

The perimeter of the square is

$\begin{array}{l}=4\left(\frac{x+5}{8x}\right)\\ =\frac{x+5}{2x}\end{array}$

Hence, the perimeter of the square is $\frac{x+5}{2x}$.

Therefore option J is the correct answer.