Area and perimeter word problem: table dimensions | Khan Academy

TL;DR

Determine the length and width of a rectangular table with a perimeter of 20 feet and an area of 24 square feet.

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: How can we solve for the length and width of the rectangular table?

We can solve for the dimensions by trying out different whole number combinations that lead to an area of 24. We then check if the corresponding perimeter equals 20.

Q: Why did we create a table to try out different combinations?

The table allows us to organize our attempts to find the right dimensions by systematically testing all possible pairs of whole numbers as length and width values.

Q: How did we determine if a combination satisfied the perimeter constraint?

We added the width and length twice, representing the sides of the rectangular table, and checked if the sum equaled 20. If it did not, we crossed out that combination.

Q: How did we find the correct dimensions of the table?

By testing all possible combinations, we discovered that a width of 4 feet and a length of 6 feet satisfy both the area and perimeter constraints.

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.