The perimeter of a square is 28 cm. Find its:
(i) one side (ii) area (iii) diagonal

Answer

To solve the problem step by step, we will find the side of the square, its area, and the length of its diagonal based on the given perimeter.

### Step 1: Find One Side of the Square
The formula for the perimeter (P) of a square is given by:
\[ P = 4a \]
where \(a\) is the length of one side of the square. We know the perimeter is 28 cm, so we can set up the equation:
\[ 28 = 4a \]
To find \(a\), we divide both sides by 4:
\[ a = \frac{28}{4} = 7 \text{ cm} \]

### Step 2: Find the Area of the Square
The area (A) of a square is calculated using the formula:
\[ A = a^2 \]
Now that we have found \(a = 7 \text{ cm}\), we can calculate the area:
\[ A = 7^2 = 49 \text{ cm}^2 \]

### Step 3: Find the Length of the Diagonal
The length of the diagonal (d) of a square can be calculated using the formula:
\[ d = a\sqrt{2} \]
Substituting the value of \(a\):
\[ d = 7\sqrt{2} \text{ cm} \]

### Summary of Results
- One side of the square: \(7 \text{ cm}\)
- Area of the square: \(49 \text{ cm}^2\)
- Length of the diagonal: \(7\sqrt{2} \text{ cm}\)

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