Doubling Playground Area Problems

The video tutorial explains how to solve a quadratic word problem involving the expansion of a playground's area. Gabriel wants to double the area of his playground by increasing all sides by the same amount. The tutorial walks through setting up the problem, formulating and solving the quadratic equation, and interpreting the results to find the new dimensions of the playground.

What is the main focus of the quadratic word problem discussed in the video?

• Reducing the area of a playground

• Finding the volume of a playground

• Doubling the area of a playground

• Calculating the perimeter of a playground

What are the initial dimensions of Gabriel's playground?

• 6 meters by 9 meters

• 5 meters by 7 meters

• 8 meters by 10 meters

• 10 meters by 12 meters

What does the variable x represent in the problem?

• The original width of the playground

• The total area of the playground

• The amount by which each side is increased

• The original length of the playground

What is the original area of the playground?

• 60 square meters

• 80 square meters

• 100 square meters

• 120 square meters

What is the target area of the playground after doubling?

• 160 square meters

• 140 square meters

• 180 square meters

• 120 square meters

What is the expression for the new width of the playground?

• 10 + 2x

• 8 + x

• 8 + 2x

• 10 + x

What is the expression for the new length of the playground?

• 8 + x

• 10 + 2x

• 8 + 2x

• 10 + x

What is the first step in solving the equation for x?

• Divide both sides by 2

• Set the equation equal to zero

• Multiply both sides by 2

• Add 160 to both sides

What method is used when factoring the equation is not feasible?

• Completing the square

• Using the quadratic formula

• Graphing the equation

• Substitution method

What is the value of x that represents the increase in each side?

• 4.0 meters

• 3.0 meters

• 2.5 meters

• 1.844 meters