Rectangle Properties and Pythagorean Theorem

The video tutorial explains how to determine the length of the diagonal of a rectangle given its area and a relationship between its width and length. It starts by setting up the problem, then uses the quadratic formula to solve for the rectangle's dimensions. Finally, it applies the Pythagorean theorem to calculate the diagonal length, rounding the result to two decimal places. The tutorial provides a comprehensive review of solving quadratic equations and applying the Pythagorean theorem.

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

• The width is 3 more than twice the length.

• The width is twice the length.

• The width is 3 less than twice the length.

• The width is half the length.

What is the formula for the area of a rectangle?

• Length + Width

• Length - Width

• Length x Width

• 2 x (Length + Width)

Which formula is used to solve the quadratic equation in this problem?

• Perimeter Formula

• Area Formula

• Quadratic Formula

• Pythagorean Theorem

What is the value of the discriminant in the quadratic equation?

• 1,033

• 289

• 256

• 128

What is the approximate value of X, the length of the rectangle?

• 8.785 cm

• 14.570 cm

• 10.5 cm

• 17.01 cm

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

• 8.785 cm

• 14.570 cm

• 17.01 cm

• 10.5 cm

Which theorem is used to find the diagonal of the rectangle?

• Perimeter Theorem

• Quadratic Theorem

• Pythagorean Theorem

• Area Theorem

What are the known lengths used in the Pythagorean theorem to find the diagonal?

• Length and Width

• Width and Diagonal

• Length and Diagonal

• Length and Height

What is the approximate length of the diagonal of the rectangle?

• 8.785 cm

• 14.570 cm

• 20.5 cm

• 17.01 cm

Why is only the positive square root considered for the diagonal length?

• Because the diagonal is always longer than the sides.

• Because the diagonal cannot be negative.

• Because the diagonal is a length.

• Because the diagonal is a width.