How Do You Find a Table’s Dimensions From Its Area and Perimeter? | Khan Academy

TL;DR

The rectangular table is 6 feet long and 4 feet wide. Its whole-number dimensions must produce an area of 24 square feet and a perimeter of 20 feet, so testing the factor pairs of 24 identifies the only pair that meets both conditions. Read on to see how each possible pair is checked and eliminated.

Transcript

Charles built a rectangular table that has a perimeter of 20 feet and an area of 24 square feet. The table is longer than it is wide. What are the length and width of the table? The length and width are whole numbers. So it's longer than it is wide. So let's draw this table here. So the table might look something like this-- where this dimension ri... Read More

Key Insights

• 🚰 The perimeter equation for a rectangular table is width + width + length + length = 20.
• 🚰 The area equation for a rectangular table is width × length = 24.
• 🍗 We can find the dimensions of the table by trying out different whole number combinations that result in an area of 24 and then checking if the corresponding perimeter equals 20.
• 👻 Trying out all possible combinations and systematically eliminating those that do not meet the constraints allows us to find the correct dimensions efficiently.
• 🦶 In this case, a width of 4 feet and a length of 6 feet satisfy both the area and perimeter requirements.
• 🎮 The process described in the video is a methodical approach that does not require advanced algebraic techniques.
• 🧑‍🏭 The understanding of factors and systematic testing can be useful in solving real-world problems that involve finding dimensions or solving equations.

Questions & Answers

Q: What are the dimensions of a rectangular table with an area of 24 square feet and a perimeter of 20 feet?

The table is 6 feet long and 4 feet wide. These dimensions give an area of 4 × 6 = 24 square feet and a perimeter of 4 + 4 + 6 + 6 = 20 feet.

Q: How can you find the table’s length and width without advanced algebra?

List the whole-number factor pairs whose product is 24, placing the larger number under length because the table is longer than it is wide. Then calculate the perimeter for each pair until it equals 20 feet.

Q: What equations represent the table’s perimeter and area?

The perimeter equation is width + width + length + length = 20. The area equation is width × length = 24.

Q: Why are the factors of 24 used to solve the problem?

The area is 24 square feet, and the length and width are whole numbers. Therefore, the possible dimensions must be whole-number factor pairs of 24.

Q: Why does a width of 1 foot and a length of 24 feet not work?

The pair has the correct area because 1 × 24 = 24. However, its perimeter is 1 + 1 + 24 + 24 = 50 feet, not 20 feet.

Q: Why does the 2-foot-by-12-foot factor pair fail?

A width of 2 feet and a length of 12 feet produces the required area of 24 square feet. Its perimeter is 2 + 2 + 12 + 12 = 28 feet, so it does not satisfy the perimeter condition.

Q: Does a width of 3 feet and a length of 8 feet satisfy both conditions?

No. Although 3 × 8 = 24 square feet, the perimeter is 3 + 3 + 8 + 8 = 22 feet rather than 20 feet.

Q: Why does the 4-foot-by-6-foot factor pair work?

A width of 4 feet and a length of 6 feet gives the required area because 4 × 6 = 24. It also gives the required perimeter because 4 + 4 + 6 + 6 = 20, and the length is greater than the width.

Summary & Key Takeaways

• Given a rectangular table with a perimeter of 20 feet and an area of 24 square feet, determine its length and width.

• The perimeter equation is width + width + length + length = 20.

• The area equation is width × length = 24.