Rectangle Dimensions and Properties

The video tutorial explains how to find the length and width of a rectangle given its perimeter and diagonal. It starts by setting up equations based on the perimeter and then expresses the length in terms of the width. The Pythagorean theorem is applied to form a quadratic equation, which is solved by factoring. The solutions for width are used to determine the length, ensuring the longer side is identified as the length.

What is the perimeter of the rectangle given in the problem?

• 50 cm

• 60 cm

• 70 cm

• 80 cm

How is the length expressed in terms of the width using the perimeter equation?

• l = w + 35

• l = 70 - 2w

• l = 2w - 70

• l = 35 - w

Which theorem is used to relate the sides of the rectangle to its diagonal?

• Euclid's Theorem

• Thales' Theorem

• Pythagorean Theorem

• Fermat's Last Theorem

What is the value of the diagonal of the rectangle?

• 30 cm

• 35 cm

• 20 cm

• 25 cm

What is the quadratic equation derived from the Pythagorean theorem?

• w^2 - 35w + 300 = 0

• w^2 + 35w - 300 = 0

• w^2 - 70w + 600 = 0

• w^2 + 70w - 600 = 0

What are the possible values for the width obtained from solving the quadratic equation?

• 10 and 25

• 15 and 20

• 20 and 25

• 15 and 30

If the width is 15 cm, what is the length of the rectangle?

• 15 cm

• 30 cm

• 20 cm

• 25 cm

If the width is 20 cm, what is the length of the rectangle?

• 20 cm

• 15 cm

• 10 cm

• 25 cm

Which side is typically considered the length in a rectangle?

• The diagonal

• The longer side

• The shorter side

• Either side

What are the final dimensions of the rectangle as concluded in the video?

• Length: 30 cm, Width: 5 cm

• Length: 15 cm, Width: 20 cm

• Length: 20 cm, Width: 15 cm

• Length: 25 cm, Width: 10 cm