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Zorluk: OrtaPerimeter and Area of 2D Figures

A square metal plate has an area of 144144 square inches. A rectangular metal plate is cut so that it has the exact same width as the square plate, but its length is twice the width of the square. What is the perimeter of the rectangular plate in inches?

  1. A
    288
  2. 72Cevap
  3. C
    48
  4. D
    36

Cevap

72
The area of the square is 144144 square inches, which means each side of the square is 1212 inches. The new rectangular plate has the same width as the square (1212 inches) and a length that is twice that width (2424 inches). To find the perimeter of the rectangle, add the length and width (12+24=3612 + 24 = 36) and multiply by 22 to account for all four sides, resulting in 7272 inches.

Adım Adım Çözüm

1
Find the side length of the original square metal plate.
Side = 1212 inches.
The area of a square is the side length squared (s2=144s^2 = 144), so the side is the square root of 144144.
2
Determine the dimensions of the rectangular plate.
Width = 1212 inches, Length = 2424 inches.
The problem states the rectangle's width equals the square's side (1212), and its length is twice that amount (2×12=242 \times 12 = 24).
3
Calculate the perimeter of the rectangular plate.
Perimeter = 2×(12+24)=722 \times (12 + 24) = 72 inches.
The perimeter of a rectangle is found by adding the length and width, then multiplying by 22.

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Perimeter and Area of 2D Figures
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Perimeter and Area of 2D Figures

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