Rectangle Dimensions and Pythagorean Theorem

The video tutorial explains how to find the height and width of a rectangle given that its width is two inches longer than its height and its diagonal measures 22 inches. The problem is solved using the Pythagorean theorem and quadratic equations. The tutorial walks through setting up the equation, applying the theorem, solving the quadratic equation, and verifying the solutions. The final height and width are approximately 14.5 inches and 16.5 inches, respectively.

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

• The width is twice the height.

• The width is equal to the height.

• The width is 2 inches shorter than the height.

• The width is 2 inches longer than the height.

What is the length of the diagonal of the rectangle?

• 20 inches

• 22 inches

• 26 inches

• 24 inches

Which theorem is used to solve for the height and width of the rectangle?

• Pythagorean theorem

• Remainder theorem

• Binomial theorem

• Fundamental theorem of calculus

What is the expression for the width of the rectangle in terms of height h?

• h - 2

• h + 2

• 2h

• h / 2

What is the equation derived from the Pythagorean theorem for this problem?

• h^2 + (h + 2)^2 = 22^2

• h^2 - (h + 2)^2 = 22^2

• h^2 + (h - 2)^2 = 22^2

• h^2 - (h - 2)^2 = 22^2

What is the simplified form of the equation before using the quadratic formula?

• 2h^2 + 4h - 480 = 0

• 2h^2 - 4h + 480 = 0

• h^2 - 2h + 240 = 0

• h^2 + 2h - 240 = 0

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

• a = 1, b = 2, c = -240

• a = 2, b = -4, c = 480

• a = 2, b = 4, c = -480

• a = 1, b = -2, c = 240

What is the approximate value of the height of the rectangle?

• 16.5 inches

• 14.5 inches

• 18.5 inches

• 12.5 inches

What is the approximate value of the width of the rectangle?

• 12.5 inches

• 14.5 inches

• 18.5 inches

• 16.5 inches

Why is the negative solution for the height excluded?

• Because it is less than zero.

• Because height cannot be negative.

• Because it is not a real number.

• Because it is greater than the width.