The side of a square shaped garden is 20 m. Find the: (a) area of the garden (b) perimeter (or boundary) of the garden (c) maximum possible distance between any two corners of the garden.

Answer

To solve the problem step by step, we will find the area, perimeter, and maximum possible distance between any two corners of the square-shaped garden.

### Step 1: Find the Area of the Garden
The area \( A \) of a square is calculated using the formula:
\[ A = \text{side}^2 \]
Given that the side of the garden is 20 m, we can substitute this value into the formula:
\[ A = 20^2 = 400 \text{ m}^2 \]

### Step 2: Find the Perimeter of the Garden
The perimeter \( P \) of a square is calculated using the formula:
\[ P = 4 \times \text{side} \]
Substituting the given side length:
\[ P = 4 \times 20 = 80 \text{ m} \]

### Step 3: Find the Maximum Possible Distance Between Any Two Corners of the Garden
The maximum distance between any two corners of a square is the length of the diagonal. We can calculate the diagonal \( d \) using the Pythagorean theorem:
\[ d = \sqrt{\text{side}^2 + \text{side}^2} \]
Substituting the side length:
\[ d = \sqrt{20^2 + 20^2} = \sqrt{400 + 400} = \sqrt{800} \]
We can simplify \( \sqrt{800} \):
\[ \sqrt{800} = \sqrt{400 \times 2} = \sqrt{400} \times \sqrt{2} = 20\sqrt{2} \text{ m} \]

### Summary of Results
(a) Area of the garden: \( 400 \text{ m}^2 \)
(b) Perimeter of the garden: \( 80 \text{ m} \)
(c) Maximum possible distance between any two corners of the garden: \( 20\sqrt{2} \text{ m} \)

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