Rectangle Dimensions and Relationships

This video tutorial addresses a geometric problem involving a rectangle where the length is three times the width, and the perimeter is 40 inches. The lesson explains how to determine the dimensions of the rectangle by setting the width as the main variable and expressing the length in terms of the width. The perimeter formula is applied to solve for the width, and subsequently, the length is calculated. The final dimensions are found to be 5 inches for the width and 15 inches for the length.

What is the main problem discussed in this lesson?

• Calculating the volume of a cube

• Solving for the diagonal of a square

• Determining the dimensions of a rectangle with a given perimeter

• Finding the area of a rectangle

What does the term 'dimensions' refer to in this context?

• The area and volume

• The perimeter and area

• The length and width

• The height and depth

Why is it important to choose a main variable when solving this problem?

• To avoid using numbers

• To make the problem more complex

• To ensure the solution is unique

• To simplify the equation

What is the relationship between the length and width of the rectangle?

• The length is twice the width

• The length is equal to the width

• The length is three times the width

• The length is half the width

Which formula is used to relate the perimeter to the dimensions of the rectangle?

• Perimeter = 2 * (Length + Width)

• Perimeter = Length * Width

• Perimeter = Length + Width

• Perimeter = 2 * Length * Width

What value is substituted for the perimeter in the equation?

• 30 inches

• 50 inches

• 40 inches

• 60 inches

How is the length expressed in terms of the width?

• Length = 2 * Width

• Length = Width / 2

• Length = Width

• Length = 3 * Width

What is the simplified equation used to solve for the width?

• 40 = 4w

• 40 = 8w

• 40 = 6w

• 40 = 10w

What is the width of the rectangle?

• 5 inches

• 6 inches

• 8 inches

• 10 inches

How is the length calculated once the width is known?

• Length = Width + 5

• Length = 2 * Width

• Length = 3 * Width

• Length = Width - 3