A square-shaped lawn has an area of 62,500 square meters. What is the cost of building a fence around it at a rate of $5.5 per meter?

Steps to Solve

1. Calculate the side length of the square lawn

Since the area of a square is given by the formula:

$$ \text{Area} = \text{side}^2 $$

we can find the side length by taking the square root of the area.

Given that the area is 62,500 square meters:

$$ \text{side} = \sqrt{62,500} $$

2. Calculate the perimeter of the square lawn

The perimeter ( P ) of a square can be calculated using the formula:

$$ P = 4 \times \text{side} $$

Substituting the side length value from the previous step:

$$ P = 4 \times \sqrt{62,500} $$

3. Calculate the total cost of building the fence

To find the total cost, we'll multiply the perimeter by the cost per meter of fencing. The cost per meter is given as $5.5:

$$ \text{Total Cost} = P \times 5.5 $$

Substituting the perimeter value:

$$ \text{Total Cost} = \left(4 \times \sqrt{62,500}\right) \times 5.5 $$

4. Perform the calculations

Now we can compute:

• First, calculate the square root: $$ \sqrt{62,500} = 250 $$

• Then compute the perimeter: $$ P = 4 \times 250 = 1000 $$

• Finally, calculate the total cost: $$ \text{Total Cost} = 1000 \times 5.5 = 5500 $$