Geometry Word Problems on Rectangles

The video tutorial addresses a geometry word problem involving a rectangle. The problem states that the length of a rectangle is two inches more than its width. If both dimensions are increased by three inches, the perimeter of the new rectangle is four inches less than eight times the width of the original rectangle. The tutorial guides viewers through drawing and labeling the rectangles, setting up and solving the equation to find the original dimensions, which are five inches by seven inches.

What is the main topic of the video?

• Algebraic equations

• Calculus

• Geometry word problem

• Trigonometry

How is the length of the rectangle related to its width?

• The length is two inches more than the width.

• The length is twice the width.

• The length is equal to the width.

• The length is half the width.

What is the purpose of drawing a sketch in the problem?

• To calculate the area.

• To find the volume.

• To visualize and label variables.

• To measure the angles.

What happens to the dimensions of the rectangle when increased by three inches?

• The dimensions remain the same.

• Both the length and width increase by three inches.

• Only the length increases.

• Only the width increases.

What is the new width of the rectangle after increasing by three inches?

• w + 2

• w + 3

• w + 4

• w + 5

What is the new length of the rectangle after increasing by three inches?

• w + 4

• w + 7

• w + 5

• w + 6

How is the perimeter of the new rectangle calculated?

• By adding the length and width.

• By multiplying the length and width.

• By subtracting the width from the length.

• By summing all four sides.

What is the formula used to calculate the perimeter of a rectangle?

• 2(l + w)

• l - w

• l * w

• l + w

What is the equation set up to find the dimensions of the original rectangle?

• 4w + 16 = 8w + 4

• 4w - 16 = 8w + 4

• 4w + 16 = 8w - 4

• 4w - 16 = 8w - 4

What does the equation 4w + 16 = 8w - 4 represent?

• The perimeter of the new rectangle.

• The relationship between the new and original perimeters.

• The volume of the rectangle.

• The area of the rectangle.