Examkin

Soru

Zorluk: KolayQuadrilaterals and Polygons

A rectangle has a length of 88 units and a width of 66 units. Which of the following statements about this rectangle must be true? Select all that apply.

  1. The area of the rectangle is 4848 square units.Cevap
  2. The length of each diagonal of the rectangle is 1010 units.Cevap
  3. The perimeter of the rectangle is 2828 units.Cevap
  4. D
    The length of each diagonal of the rectangle is 1414 units.
  5. E
    The area of the rectangle is 2828 square units.

Cevap

The correct statements are that the area of the rectangle is 48 square units, the length of each diagonal is 10 units, and the perimeter of the rectangle is 28 units.
The statement regarding the area being 48 square units is correct because 8×6=488 \times 6 = 48. The statement regarding the diagonal being 10 units is correct because 82+62=10\sqrt{8^2 + 6^2} = 10. The statement regarding the perimeter being 28 units is correct because 2×(8+6)=282 \times (8 + 6) = 28.

Adım Adım Çözüm

1
Calculate the area of the rectangle
Area=8×6=48\text{Area} = 8 \times 6 = 48 square units
The area formula for a rectangle is length multiplied by width.
2
Calculate the length of the diagonal using the Pythagorean theorem
Diagonal=82+62=64+36=10\text{Diagonal} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = 10 units
The sides and diagonal of a rectangle form a right triangle where the diagonal is the hypotenuse.
3
Calculate the perimeter of the rectangle
Perimeter=2×(8+6)=28\text{Perimeter} = 2 \times (8 + 6) = 28 units
The perimeter formula for a rectangle is twice the sum of its length and width.

Anahtar Kavram

Basic geometric properties of rectangles including area, perimeter, and diagonal calculation via the Pythagorean theorem.
Bu soruyu puanla

Konular

Quadrilaterals and Polygons

Bu konudan daha fazla soru