Understanding the Square Area and Perimeter Problem

The question asks us to find the perimeter of a square given its area. We are given that the area of the square is 625 square centimeters (cm²). We need to determine which of the provided options represents the correct perimeter.

Square Formulas Explained

To solve this, we need to know the basic formulas related to a square:

• Area of a Square: The area ($A$) is calculated by multiplying the length of a side ($s$) by itself. The formula is $A = s^2$.
• Perimeter of a Square: The perimeter ($P$) is the total length of all sides added together. Since a square has 4 equal sides, the formula is $P = 4s$.

Calculating the Square's Side Length

We are given the area ($A$) = 625 cm². We can use the area formula to find the side length ($s$):

1. Start with the area formula: $A = s^2$.
2. Substitute the given area: $625 \text{ cm}^2 = s^2$.
3. To find the side length ($s$), take the square root of both sides: $s = \sqrt{625 \text{ cm}^2}$.
4. Calculate the square root: $s = 25$ cm.

So, the length of one side of the square is 25 cm.

Calculating the Square's Perimeter

Now that we know the side length ($s = 25$ cm), we can calculate the perimeter ($P$) using the perimeter formula:

1. Start with the perimeter formula: $P = 4s$.
2. Substitute the side length we found: $P = 4 \times 25 \text{ cm}$.
3. Calculate the result: $P = 100$ cm.

The perimeter of the square is 100 cm.

Comparing with Options

Let's compare our calculated perimeter with the given options:

• Option 1: 100 cm
• Option 2: 125 cm
• Option 3: 75 cm
• Option 4: 80 cm

Our calculated perimeter matches Option 1.