Understanding Perimeter of a Rectangle

The video tutorial explains how to find the perimeter of a rectangle using a rational expression. It begins with a review of the perimeter concept, then formulates an expression using given length and width. The tutorial discusses domain constraints, specifically when the denominator becomes zero, and simplifies the expression step-by-step. The final simplified expression is presented, with a note on factoring options.

What is the perimeter of a rectangle?

• The length of the rectangle

• The distance around the rectangle

• The width of the rectangle

• The area inside the rectangle

If a rectangle has a length 'l' and width 'w', how is the perimeter expressed?

• 2l + 2w

• l - w

• l + w

• l * w

What is the expression for the perimeter if the length is (2x + 5y)/(x + 4) and the width is (x - 3y)/(x + 4)?

• (2x + 5y)/(x + 4) + (x - 3y)/(x + 4)

• (2x + 5y) + (x - 3y)

• 2(2x + 5y)/(x + 4) + 2(x - 3y)/(x + 4)

• 2(2x + 5y) + 2(x - 3y)

What value of 'x' makes the denominator zero in the given expressions?

• 2

• 4

• 0

• -4

Why is it important to constrain the domain in this problem?

• To calculate the area

• To ensure the expressions are defined

• To find the perimeter

• To simplify the expressions

What is the result of distributing 2 in the expression 2(2x + 5y)?

• 4x + 5y

• 4x + 10y

• 2x + 5y

• 2x + 10y

What is the common denominator used when adding the rational expressions?

• x - 4

• x - 3y

• x + 4

• 2x + 5y

What is the simplified expression for the perimeter after adding the rational expressions?

• 6x + 4y

• 4x + 6y

• 6x - 4y

• 4x - 6y

What can be factored out from the final simplified expression for the perimeter?

• 6

• 2

• 4

• 3

What is the final expression for the perimeter after factoring?

• 6x + 4y

• 2x + 3y

• 2(3x + 2y)

• 3x + 2y