Q5 PT. - Algebra 1

Question

The length of the side of a square is given by the function $s=\sqrt{A}$, where A is the area of the square. What is the perimeter of a square that has an area of 64 square inches?

 

A 64 inches                                  C 32 inches               

B 8 inches                                    D 16 inches

Step-by-Step Solution

Answer

The perimeter of a square that has an area of 64 square inches is 32 inches.

Option C is correct.

Step 1. State the concept of perimeter of the square.

The perimeter of a square is the sum of length of all sides of the square.

Suppose, the length of the side of square is ‘s’, then the perimeter of the square (P) is given as:

 

$P=4s \dots \left(1\right)$

Step 2. State the concept of Area of square.

Area of a square is its length times width. Since all sides of square are equal, the area of the square is the square of its length.

 

Suppose, the length of the side of square is ‘s’, then the area of the square(A) is given as:

 

$A=s^2\dots \left(2\right)$

Step 3. Calculate the perimeter.

The length of the side of a square is given by the function $s=\sqrt{A}$, where A is the area of the square.

 

Now to find the perimeter of the square whose area is 64 square inches, first find the length of sides of the square.

 

Substitute $A=64$ in $s=\sqrt{A}$ to find the length of sides of the square.

 

$$\begin{gathered} s=\sqrt{A} \\ =\sqrt{64} \\ =8 \end{gathered}$$

 

Therefore, the length of sides of the square is 8 inches.

 

Now substitute $s=8$ in (1) to get the perimeter of the square.

$$\begin{gathered} P=4s \\ =4\left(8\right) \\ =32 \end{gathered}$$

 

Therefore, the perimeter of the square is 32 inches.

Option C is correct.