A Picnic Table Is In The Shape Of A Rectangle That Is 12 Feet Long And 4 Feet Wide. What Is The Length Of A Diagonal Of The Table? Round To The Nearest Tenth.

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Introduction

A picnic table is a common outdoor furniture piece that is often used for social gatherings and meals. In this article, we will explore the mathematical concept of calculating the diagonal of a rectangle, using a picnic table as an example. We will use the dimensions of a typical picnic table, which is 12 feet long and 4 feet wide, to calculate the length of the diagonal.

Understanding the Problem

To calculate the diagonal of a rectangle, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem

The Pythagorean theorem can be expressed mathematically as:

a^2 + b^2 = c^2

where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse (the diagonal of the rectangle).

Applying the Pythagorean Theorem

In our example, the picnic table is a rectangle with a length of 12 feet and a width of 4 feet. We can use the Pythagorean theorem to calculate the length of the diagonal.

Let's substitute the values into the equation:

a^2 + b^2 = c^2 12^2 + 4^2 = c^2 144 + 16 = c^2 160 = c^2

Solving for c

To find the length of the diagonal, we need to take the square root of both sides of the equation:

c = √160 c ≈ 12.65

Rounding to the Nearest Tenth

The problem asks us to round the answer to the nearest tenth. Therefore, we round 12.65 to 12.7.

Conclusion

In this article, we used the Pythagorean theorem to calculate the length of the diagonal of a picnic table. We found that the diagonal is approximately 12.7 feet long. This calculation can be applied to any rectangle, and it is a useful tool for architects, engineers, and designers who need to calculate the dimensions of a rectangle.

Real-World Applications

The Pythagorean theorem has many real-world applications, including:

  • Architecture: Architects use the Pythagorean theorem to calculate the dimensions of buildings, bridges, and other structures.
  • Engineering: Engineers use the Pythagorean theorem to calculate the stress and strain on materials, and to design safe and efficient structures.
  • Design: Designers use the Pythagorean theorem to calculate the dimensions of products, such as furniture and packaging.

Practice Problems

Here are a few practice problems to help you apply the Pythagorean theorem:

  • A rectangle has a length of 15 feet and a width of 8 feet. What is the length of the diagonal?
  • A rectangle has a length of 20 feet and a width of 6 feet. What is the length of the diagonal?
  • A rectangle has a length of 18 feet and a width of 10 feet. What is the length of the diagonal?

Answer Key

Here are the answers to the practice problems:

  • 19.2 feet
  • 22.4 feet
  • 20.6 feet

Conclusion

Introduction

In our previous article, we explored the mathematical concept of calculating the diagonal of a rectangle using the Pythagorean theorem. We used a picnic table as an example and calculated the length of the diagonal to be approximately 12.7 feet. In this article, we will answer some frequently asked questions about calculating the diagonal of a rectangle.

Q&A

Q: What is the Pythagorean theorem?

A: The Pythagorean theorem is a mathematical concept that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Q: How do I apply the Pythagorean theorem to calculate the diagonal of a rectangle?

A: To apply the Pythagorean theorem, you need to substitute the values of the two sides that form the right angle into the equation a^2 + b^2 = c^2, where a and b are the lengths of the two sides, and c is the length of the diagonal.

Q: What if I don't have a calculator?

A: You can still calculate the diagonal of a rectangle without a calculator. You can use the Pythagorean theorem to calculate the square of the diagonal, and then take the square root of the result.

Q: Can I use the Pythagorean theorem to calculate the diagonal of a square?

A: Yes, you can use the Pythagorean theorem to calculate the diagonal of a square. However, since a square has all sides equal, you can simply use the formula d = s√2, where d is the diagonal and s is the length of a side.

Q: What if I have a rectangle with a length of 10 feet and a width of 5 feet?

A: To calculate the diagonal of a rectangle with a length of 10 feet and a width of 5 feet, you can use the Pythagorean theorem:

a^2 + b^2 = c^2 10^2 + 5^2 = c^2 100 + 25 = c^2 125 = c^2

c = √125 c ≈ 11.18

Q: Can I use the Pythagorean theorem to calculate the diagonal of a triangle that is not a right triangle?

A: No, the Pythagorean theorem only applies to right triangles. If you have a triangle that is not a right triangle, you will need to use a different method to calculate the length of the diagonal.

Q: What if I have a rectangle with a length of 15 feet and a width of 8 feet?

A: To calculate the diagonal of a rectangle with a length of 15 feet and a width of 8 feet, you can use the Pythagorean theorem:

a^2 + b^2 = c^2 15^2 + 8^2 = c^2 225 + 64 = c^2 289 = c^2

c = √289 c ≈ 17

Q: Can I use the Pythagorean theorem to calculate the diagonal of a circle?

A: No, the Pythagorean theorem only applies to rectangles and right triangles. If you have a circle, you will need to use a different method to calculate the length of the diagonal.

Conclusion

In this article, we answered some frequently asked questions about calculating the diagonal of a rectangle using the Pythagorean theorem. We provided examples and explanations to help readers understand the concept and apply it to different scenarios.