A Rectangle Has An Area Of 128 Cm². If The Width Is 8 Cm, The Length Of The Rectangle Is. . .
Introduction
In mathematics, a rectangle is a type of quadrilateral with four right angles and opposite sides of equal length. The area of a rectangle is calculated by multiplying its length and width. In this problem, we are given the area of a rectangle as 128 cm² and the width as 8 cm. We need to find the length of the rectangle.
Formula for the Area of a Rectangle
The formula for the area of a rectangle is:
Area = Length × Width
In this problem, we are given the area as 128 cm² and the width as 8 cm. We can plug these values into the formula to get:
128 = Length × 8
Solving for the Length
To solve for the length, we need to isolate the length variable. We can do this by dividing both sides of the equation by 8:
Length = 128 ÷ 8
Length = 16
Conclusion
Therefore, the length of the rectangle is 16 cm.
Real-World Applications
This problem has real-world applications in various fields such as architecture, engineering, and design. For example, in building design, architects need to calculate the area of rectangles to determine the amount of materials needed for construction. In engineering, engineers need to calculate the area of rectangles to determine the stress and strain on structures.
Tips and Tricks
Here are some tips and tricks to help you solve this problem:
- Make sure to read the problem carefully and understand what is being asked.
- Use the formula for the area of a rectangle to solve the problem.
- Check your units to make sure they are consistent.
- Use a calculator to check your answer.
Practice Problems
Here are some practice problems to help you practice solving this type of problem:
- A rectangle has an area of 240 cm² and a width of 12 cm. What is the length of the rectangle?
- A rectangle has an area of 180 cm² and a length of 15 cm. What is the width of the rectangle?
Solutions to Practice Problems
Here are the solutions to the practice problems:
- A rectangle has an area of 240 cm² and a width of 12 cm. To solve for the length, we can use the formula for the area of a rectangle:
240 = Length × 12
Length = 240 ÷ 12
Length = 20
Therefore, the length of the rectangle is 20 cm.
- A rectangle has an area of 180 cm² and a length of 15 cm. To solve for the width, we can use the formula for the area of a rectangle:
180 = Width × 15
Width = 180 ÷ 15
Width = 12
Therefore, the width of the rectangle is 12 cm.
Conclusion
In conclusion, this problem is a simple application of the formula for the area of a rectangle. By plugging in the given values and solving for the length, we can find the answer to the problem. This problem has real-world applications in various fields and can be used to practice solving similar problems.
References
- [1] "Geometry" by Michael Artin
- [2] "Mathematics for the Nonmathematician" by Morris Kline
Related Topics
Area of a Square
A square is a type of rectangle with all sides of equal length. The area of a square is calculated by multiplying the length of one side by itself.
Area = Side × Side
For example, if the side of a square is 10 cm, the area would be:
Area = 10 × 10
Area = 100 cm²
Perimeter of a Rectangle
The perimeter of a rectangle is the distance around the rectangle. It is calculated by adding up the lengths of all four sides.
Perimeter = 2 × (Length + Width)
For example, if the length of a rectangle is 20 cm and the width is 10 cm, the perimeter would be:
Perimeter = 2 × (20 + 10)
Perimeter = 2 × 30
Perimeter = 60 cm
Area of a Triangle
A triangle is a type of polygon with three sides. The area of a triangle is calculated by using the formula:
Area = (Base × Height) ÷ 2
For example, if the base of a triangle is 10 cm and the height is 5 cm, the area would be:
Area = (10 × 5) ÷ 2
Area = 50 ÷ 2
Area = 25 cm²
Q&A
Q: What is the formula for the area of a rectangle?
A: The formula for the area of a rectangle is Area = Length × Width.
Q: How do I solve for the length of a rectangle if I know the area and width?
A: To solve for the length, you can use the formula Length = Area ÷ Width.
Q: What if I know the length and width of a rectangle, but not the area? How do I find the area?
A: To find the area, you can use the formula Area = Length × Width.
Q: What is the difference between a rectangle and a square?
A: A rectangle is a type of quadrilateral with four right angles and opposite sides of equal length, but not all sides are equal in length. A square is a type of rectangle with all sides of equal length.
Q: How do I find the perimeter of a rectangle?
A: To find the perimeter of a rectangle, you can use the formula Perimeter = 2 × (Length + Width).
Q: What is the area of a square with a side length of 10 cm?
A: To find the area of a square, you can use the formula Area = Side × Side. In this case, the area would be Area = 10 × 10 = 100 cm².
Q: What is the perimeter of a rectangle with a length of 20 cm and a width of 10 cm?
A: To find the perimeter of a rectangle, you can use the formula Perimeter = 2 × (Length + Width). In this case, the perimeter would be Perimeter = 2 × (20 + 10) = 2 × 30 = 60 cm.
Q: How do I find the area of a triangle?
A: To find the area of a triangle, you can use the formula Area = (Base × Height) ÷ 2.
Q: What is the area of a triangle with a base of 10 cm and a height of 5 cm?
A: To find the area of a triangle, you can use the formula Area = (Base × Height) ÷ 2. In this case, the area would be Area = (10 × 5) ÷ 2 = 50 ÷ 2 = 25 cm².
Q: Can I use the formula for the area of a rectangle to find the area of a square?
A: Yes, you can use the formula for the area of a rectangle to find the area of a square. Since a square is a type of rectangle with all sides of equal length, you can use the formula Area = Length × Width and plug in the same value for both the length and width.
Q: What if I know the area of a rectangle, but not the length or width? How do I find the length and width?
A: To find the length and width, you can use the formula Area = Length × Width and try different combinations of length and width that would result in the same area.
Q: Can I use the formula for the perimeter of a rectangle to find the perimeter of a square?
A: Yes, you can use the formula for the perimeter of a rectangle to find the perimeter of a square. Since a square is a type of rectangle with all sides of equal length, you can use the formula Perimeter = 2 × (Length + Width) and plug in the same value for both the length and width.
Q: What if I know the perimeter of a rectangle, but not the length or width? How do I find the length and width?
A: To find the length and width, you can use the formula Perimeter = 2 × (Length + Width) and try different combinations of length and width that would result in the same perimeter.
Conclusion
In conclusion, this article has provided a comprehensive guide to solving problems involving the area and perimeter of rectangles and squares. By using the formulas for the area and perimeter of these shapes, you can solve a wide range of problems and apply your knowledge to real-world situations.
References
- [1] "Geometry" by Michael Artin
- [2] "Mathematics for the Nonmathematician" by Morris Kline