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Zorluk: OrtaPerimeter and Area of 2D Figures

A rectangular garden has a perimeter of 5656 meters. The length of the garden is 44 meters greater than its width. If a 33-meter wide paved path is built entirely inside the garden along all four of its borders, what is the area, in square meters, of the remaining unpaved section of the garden?

Cevap: 60 square meters

Cevap

The area of the remaining unpaved section of the garden is 60 square meters.
The original dimensions of the garden are found to be 12 meters and 16 meters based on the given perimeter and side relationships. The inner unpaved section has dimensions of 12 - 6 = 6 meters and 16 - 6 = 10 meters because the 3-meter path cuts into both sides of each dimension. Multiplying these inner dimensions yields a final area of 60 square meters.

Adım Adım Çözüm

1
Use the perimeter formula to find the outer length and width of the garden.
Width = 12 meters, Length = 16 meters.
The relationship between length and width (L = W + 4) and the total perimeter formula 2L+2W=562L + 2W = 56 allows us to find the exact dimensions.
2
Calculate the dimensions of the inner unpaved area by subtracting the path's width.
Inner width = 6 meters, Inner length = 10 meters.
The 3-meter path runs along all four borders, meaning the path's width must be subtracted twice (3 + 3 = 6 meters) from both the outer length and the outer width.
3
Calculate the final area of the inner unpaved section.
60 square meters.
The area of a rectangle is found by multiplying its length by its width (10×610 \times 6).

Anahtar Kavram

Solving for unknown dimensions using perimeter, and determining the area of a smaller inscribed rectangle by correctly subtracting border widths.
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Perimeter and Area of 2D Figures

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