A Rectangle Has An Area Of 77 Square Inches And A Width Of 5.5 Inches.What Is The Length, I I I , Of This Rectangle?A. I = 14 In I = 14 \text{ In} I = 14 In B. I = 22 In I = 22 \text{ In} I = 22 In C. I = 33 In I = 33 \text{ In} I = 33 In D. I = 63 In I = 63 \text{ In} I = 63 In

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Introduction

In geometry, a rectangle is a four-sided shape with opposite sides of equal length. The area of a rectangle is calculated by multiplying its length and width. In this article, we will explore how to find the length of a rectangle given its area and width.

The Formula for the Area of a Rectangle

The area of a rectangle is given by the formula:

Area = Length × Width

In this case, we are given the area of the rectangle as 77 square inches and the width as 5.5 inches. We need to find the length, denoted by the variable II.

Finding the Length

To find the length, we can rearrange the formula for the area of a rectangle to solve for the length:

Length = Area ÷ Width

Substituting the given values, we get:

Length = 77 ÷ 5.5

Calculating the Length

To calculate the length, we can divide 77 by 5.5:

Length = 14.0

Conclusion

Therefore, the length of the rectangle is 14 inches.

Answer

The correct answer is:

  • A. I=14 inI = 14 \text{ in}

Discussion

This problem is a classic example of how to use algebra to solve a geometric problem. By rearranging the formula for the area of a rectangle, we can solve for the length. This type of problem is commonly encountered in mathematics and is an essential skill to have in geometry.

Real-World Applications

In real-world applications, finding the length of a rectangle is crucial in various fields such as architecture, engineering, and design. For example, in building design, architects need to calculate the length of a room to determine the amount of materials needed for construction.

Tips and Tricks

When solving problems like this, it's essential to:

  • Read the problem carefully and understand what is given and what is asked.
  • Use algebraic manipulations to solve for the unknown variable.
  • Check your calculations to ensure accuracy.

Practice Problems

Try solving the following problems:

  • A rectangle has an area of 120 square inches and a width of 6 inches. What is the length?
  • A rectangle has an area of 90 square inches and a width of 5 inches. What is the length?

Conclusion

In conclusion, finding the length of a rectangle given its area and width is a straightforward process that involves algebraic manipulations. By following the steps outlined in this article, you can solve similar problems with ease.

References

  • [1] Geometry: A Comprehensive Introduction
  • [2] Algebra: A First Course
  • [3] Mathematics for Engineers and Scientists

Related Articles

  • [A Circle's Area and Radius: Finding the Diameter](link to article)
  • [A Triangle's Area and Base: Finding the Height](link to article)

Comments

Please leave your comments and feedback below. Do you have any questions or topics you'd like to discuss?

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Introduction

In our previous article, we explored how to find the length of a rectangle given its area and width. In this article, we will answer some frequently asked questions related to this topic.

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 find the length of a rectangle given its area and width?

A: To find the length, you can rearrange the formula for the area of a rectangle to solve for the length:

Length = Area ÷ Width

Q: What if the width is not a whole number?

A: If the width is not a whole number, you can still find the length by dividing the area by the width. For example, if the area is 77 square inches and the width is 5.5 inches, you can divide 77 by 5.5 to get the length.

Q: Can I use this formula to find the length of a rectangle with a negative width?

A: No, you cannot use this formula to find the length of a rectangle with a negative width. The width of a rectangle is always a positive number.

Q: What if I have a rectangle with a width of 0 inches?

A: If you have a rectangle with a width of 0 inches, the area would be 0 square inches. In this case, the length would also be 0 inches.

Q: Can I use this formula to find the length of a rectangle with a fractional width?

A: Yes, you can use this formula to find the length of a rectangle with a fractional width. For example, if the area is 77 square inches and the width is 5.5 inches, you can divide 77 by 5.5 to get the length.

Q: What if I have a rectangle with a width of 1 inch?

A: If you have a rectangle with a width of 1 inch, the area would be equal to the length. In this case, the length would also be equal to the area.

Examples

Example 1:

A rectangle has an area of 120 square inches and a width of 6 inches. What is the length?

Length = Area ÷ Width Length = 120 ÷ 6 Length = 20 inches

Example 2:

A rectangle has an area of 90 square inches and a width of 5 inches. What is the length?

Length = Area ÷ Width Length = 90 ÷ 5 Length = 18 inches

Conclusion

In conclusion, finding the length of a rectangle given its area and width is a straightforward process that involves algebraic manipulations. By following the steps outlined in this article, you can solve similar problems with ease.

References

  • [1] Geometry: A Comprehensive Introduction
  • [2] Algebra: A First Course
  • [3] Mathematics for Engineers and Scientists

Related Articles

  • [A Circle's Area and Radius: Finding the Diameter](link to article)
  • [A Triangle's Area and Base: Finding the Height](link to article)

Comments

Please leave your comments and feedback below. Do you have any questions or topics you'd like to discuss?

Additional Resources

  • [Online Calculator](link to online calculator)
  • [Mathematics Tutorials](link to mathematics tutorials)
  • [Geometry Problems](link to geometry problems)

FAQs

  • 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 find the length of a rectangle given its area and width? A: To find the length, you can rearrange the formula for the area of a rectangle to solve for the length: Length = Area ÷ Width.
  • Q: What if the width is not a whole number? A: If the width is not a whole number, you can still find the length by dividing the area by the width.