Rectangle Area and Dimensions Problems

The video tutorial by Patrick covers solving quadratic equations through a word problem involving the area of rectangles. The problem is divided into two parts, A and B, each requiring the determination of x values that satisfy the area condition. Part A involves factoring a quadratic equation with a coefficient, while Part B is simpler due to the absence of a coefficient. The solutions are verified by checking if they make sense in the context of the problem, ensuring no negative lengths or widths.

What is the main objective of the word problem discussed in the video?

• To calculate the volume of a cube

• To find the value of x for a given area

• To find the perimeter of a rectangle

• To determine the circumference of a circle

What is the formula for the area of a rectangle?

• Length + Width

• Length x Width

• Length x Height

• 2 x (Length + Width)

What is the length of the first rectangle in terms of x?

• x + 5

• x + 6

• 2x - 5

• 2x + 6

What is the width of the first rectangle in terms of x?

• 2x - 5

• x + 6

• x + 5

• 2x + 6

What is the first step in solving the quadratic equation for the first rectangle?

• Subtract 42 from both sides

• Add 42 to both sides

• Expand and simplify the equation

• Divide both sides by x

What is the expanded form of the quadratic equation for the first rectangle?

• 2x^2 + 7x - 72 = 0

• x^2 - 7x + 72 = 0

• x^2 + 7x - 72 = 0

• 2x^2 - 7x + 72 = 0

What are the values of a, b, and c in the quadratic equation for the first rectangle?

• a = 1, b = 7, c = -72

• a = 1, b = -7, c = 72

• a = 2, b = -7, c = 72

• a = 2, b = 7, c = -72

What are the two numbers that multiply to -144 and add up to 7?

• 8 and -18

• -8 and 18

• 9 and -16

• -9 and 16

What is the factored form of the quadratic equation for the first rectangle?

• (2x - 9)(x + 8)

• (2x + 9)(x - 8)

• (x - 9)(x + 8)

• (x + 9)(x - 8)

What is the valid solution for x in the first rectangle problem?

• x = -8

• x = 9

• x = 0

• x = 4.5