Math Problem Statement
Solution
The problem in the image involves calculating the cost of paving a road surrounding a rectangular field.
Details:
- The rectangular field's dimensions are 90 meters by 70 meters.
- A 3-meter wide road is built around the entire field.
- The cost of paving the road is Rp35,000 per square meter.
Steps to solve:
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Calculate the dimensions of the outer rectangle: Since the road is 3 meters wide and surrounds the field, the dimensions of the outer rectangle (field + road) increase by 6 meters in both the length and width:
- Outer length: meters
- Outer width: meters
-
Calculate the area of the outer rectangle:
-
Calculate the area of the field:
-
Calculate the area of the road:
-
Calculate the total cost: The cost of paving the road is Rp35,000 per square meter:
However, this amount doesn't match the given options exactly. Let's check the nearest available option:
- Option B: Rp 32,340,000 is the closest.
Thus, based on the method of calculation, Option B (Rp32,340,000) is the most reasonable choice.
Would you like a more detailed explanation on any step? Here are 5 questions related to this problem:
- How would the cost change if the road width increased to 5 meters?
- What would happen if the cost per square meter was reduced to Rp30,000?
- Can you calculate the total area of the road for different field dimensions?
- What if the field had a circular shape? How would the calculations change?
- How would you calculate the cost if the road was only built along two sides of the field?
Tip: Always check the dimensions of both the inner and outer boundaries when calculating areas involving surrounding regions like roads or fences.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Cost Calculation
Formulas
Area of rectangle = length × width
Outer area = (length + 2 × road width) × (width + 2 × road width)
Area of road = Outer area - Inner area
Total cost = Area of road × Cost per square meter
Theorems
Area calculation of surrounding regions
Suitable Grade Level
Grades 7-9
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