1. Find The Cost Of Fencing A Square Park With A Side Length Of 250 M At A Rate Of 80 Per Metre.2. A Square Sheet Of Paper Has A Perimeter Of 40 Cm. What Is The Length Of Its Sides?

Mar 1, 2025 by ADMIN 182 views

Mathematical Calculations: Finding the Cost of Fencing a Square Park and Determining the Length of a Square Sheet of Paper

1. Find the Cost of Fencing a Square Park with a Side Length of 250 m at a Rate of 80 per Metre

Calculating the Perimeter of a Square To find the cost of fencing a square park, we first need to calculate the perimeter of the square. The perimeter of a square is given by the formula: perimeter = 4 × side length. In this case, the side length of the square park is 250 m.

Perimeter = 4 × side length
Perimeter = 4 × 250 m
Perimeter = 1000 m

Calculating the Cost of Fencing Now that we have the perimeter of the square park, we can calculate the cost of fencing. The cost of fencing is given by the formula: cost = perimeter × rate per metre. In this case, the rate per metre is 80.

Cost = perimeter × rate per metre
Cost = 1000 m × 80 per metre
Cost = 80000

Therefore, the cost of fencing a square park with a side length of 250 m at a rate of 80 per metre is 80,000.

2. A Square Sheet of Paper Has a Perimeter of 40 cm. What is the Length of Its Sides?

Understanding the Relationship Between Perimeter and Side Length To find the length of the sides of a square sheet of paper, we need to understand the relationship between the perimeter and the side length of a square. The perimeter of a square is given by the formula: perimeter = 4 × side length.

Calculating the Side Length Now that we have the perimeter of the square sheet of paper, we can calculate the side length. We can rearrange the formula to solve for the side length: side length = perimeter ÷ 4.

Side length = perimeter ÷ 4
Side length = 40 cm ÷ 4
Side length = 10 cm

Therefore, the length of the sides of a square sheet of paper with a perimeter of 40 cm is 10 cm.

Mathematical Formulas and Calculations

Perimeter of a Square The perimeter of a square is given by the formula: perimeter = 4 × side length.

Cost of Fencing The cost of fencing is given by the formula: cost = perimeter × rate per metre.

Side Length of a Square The side length of a square is given by the formula: side length = perimeter ÷ 4.

Real-World Applications of Mathematical Calculations

Fencing a Square Park The cost of fencing a square park can be calculated using the formula: cost = perimeter × rate per metre. This calculation is essential for determining the budget required for fencing a square park.

Determining the Length of a Square Sheet of Paper The length of the sides of a square sheet of paper can be calculated using the formula: side length = perimeter ÷ 4. This calculation is essential for determining the dimensions of a square sheet of paper.

Conclusion

In conclusion, mathematical calculations play a crucial role in determining the cost of fencing a square park and the length of the sides of a square sheet of paper. By using the formulas: perimeter = 4 × side length, cost = perimeter × rate per metre, and side length = perimeter ÷ 4, we can calculate the cost of fencing and the length of the sides of a square sheet of paper.

Future Research Directions

Optimizing Fencing Costs Future research can focus on optimizing fencing costs by exploring alternative materials and methods for fencing a square park.

Determining the Dimensions of a Square Sheet of Paper Future research can focus on determining the dimensions of a square sheet of paper using different formulas and calculations.

References

[1] "Mathematics for Dummies" by Mark Ryan
[2] "Geometry: A Comprehensive Introduction" by Dan Pedoe
[3] "Calculus: Early Transcendentals" by James Stewart

Glossary

Perimeter: The distance around a square or rectangle.
Side length: The length of one side of a square or rectangle.
Rate per metre: The cost of fencing per metre.
Cost: The total cost of fencing a square park.

Appendix

Mathematical Formulas and Calculations
Real-World Applications of Mathematical Calculations
Conclusion
Future Research Directions
References
Glossary
Appendix

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Mathematical Calculations: Q&A

Q1: What is the perimeter of a square with a side length of 300 m?

A1: To find the perimeter of a square, we use the formula: perimeter = 4 × side length. In this case, the side length is 300 m.

Perimeter = 4 × side length
Perimeter = 4 × 300 m
Perimeter = 1200 m

Therefore, the perimeter of a square with a side length of 300 m is 1200 m.

Q2: A square sheet of paper has a perimeter of 60 cm. What is the length of its sides?

A2: To find the length of the sides of a square sheet of paper, we use the formula: side length = perimeter ÷ 4. In this case, the perimeter is 60 cm.

Side length = perimeter ÷ 4
Side length = 60 cm ÷ 4
Side length = 15 cm

Therefore, the length of the sides of a square sheet of paper with a perimeter of 60 cm is 15 cm.

Q3: What is the cost of fencing a square park with a side length of 200 m at a rate of 100 per metre?

A3: To find the cost of fencing a square park, we use the formula: cost = perimeter × rate per metre. First, we need to find the perimeter of the square park.

Perimeter = 4 × side length
Perimeter = 4 × 200 m
Perimeter = 800 m

Now, we can calculate the cost of fencing.

Cost = perimeter × rate per metre
Cost = 800 m × 100 per metre
Cost = 80000

Therefore, the cost of fencing a square park with a side length of 200 m at a rate of 100 per metre is 80,000.

Q4: A square has a perimeter of 80 cm. What is the length of its sides?

A4: To find the length of the sides of a square, we use the formula: side length = perimeter ÷ 4. In this case, the perimeter is 80 cm.

Side length = perimeter ÷ 4
Side length = 80 cm ÷ 4
Side length = 20 cm

Therefore, the length of the sides of a square with a perimeter of 80 cm is 20 cm.

Q5: What is the perimeter of a square with a side length of 400 m?

A5: To find the perimeter of a square, we use the formula: perimeter = 4 × side length. In this case, the side length is 400 m.

Perimeter = 4 × side length
Perimeter = 4 × 400 m
Perimeter = 1600 m

Therefore, the perimeter of a square with a side length of 400 m is 1600 m.

Q6: A square sheet of paper has a perimeter of 80 cm. What is the length of its sides?

A6: To find the length of the sides of a square sheet of paper, we use the formula: side length = perimeter ÷ 4. In this case, the perimeter is 80 cm.

Side length = perimeter ÷ 4
Side length = 80 cm ÷ 4
Side length = 20 cm

Therefore, the length of the sides of a square sheet of paper with a perimeter of 80 cm is 20 cm.

Q7: What is the cost of fencing a square park with a side length of 250 m at a rate of 80 per metre?

A7: To find the cost of fencing a square park, we use the formula: cost = perimeter × rate per metre. First, we need to find the perimeter of the square park.

Perimeter = 4 × side length
Perimeter = 4 × 250 m
Perimeter = 1000 m

Now, we can calculate the cost of fencing.

Cost = perimeter × rate per metre
Cost = 1000 m × 80 per metre
Cost = 80000

Therefore, the cost of fencing a square park with a side length of 250 m at a rate of 80 per metre is 80,000.

Q8: A square has a perimeter of 100 cm. What is the length of its sides?

A8: To find the length of the sides of a square, we use the formula: side length = perimeter ÷ 4. In this case, the perimeter is 100 cm.

Side length = perimeter ÷ 4
Side length = 100 cm ÷ 4
Side length = 25 cm

Therefore, the length of the sides of a square with a perimeter of 100 cm is 25 cm.

Q9: What is the perimeter of a square with a side length of 500 m?

A9: To find the perimeter of a square, we use the formula: perimeter = 4 × side length. In this case, the side length is 500 m.

Perimeter = 4 × side length
Perimeter = 4 × 500 m
Perimeter = 2000 m

Therefore, the perimeter of a square with a side length of 500 m is 2000 m.

Q10: A square sheet of paper has a perimeter of 60 cm. What is the length of its sides?

A10: To find the length of the sides of a square sheet of paper, we use the formula: side length = perimeter ÷ 4. In this case, the perimeter is 60 cm.

Side length = perimeter ÷ 4
Side length = 60 cm ÷ 4
Side length = 15 cm