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Answer :
To solve this problem, we need to find the actual area of the space for Joseph's new grill in square inches using the provided scale. Here's a step-by-step solution:
1. Understand the Scale:
- The scale given is 2 cm for every 5 inches.
2. Dimensions of the Grill Space in the Drawing:
- Length in the drawing: 10 cm
- Width in the drawing: 18 cm
3. Convert the Drawing Dimensions to Actual Dimensions:
- First, we need to determine the conversion factor from centimeters to inches, based on the scale.
- For every 2 cm in the drawing, it corresponds to 5 inches in actual size.
4. Conversion Factor Calculation:
- [tex]\( \text{Conversion factor (inches per cm)} = \frac{5 \text{ inches}}{2 \text{ cm}} \)[/tex]
- [tex]\( \text{Conversion factor} = 2.5 \text{ inches per cm} \)[/tex]
5. Convert the Length and Width to Inches:
- Actual length: [tex]\( 10 \text{ cm} \times 2.5 \text{ inches per cm} = 25 \text{ inches} \)[/tex]
- Actual width: [tex]\( 18 \text{ cm} \times 2.5 \text{ inches per cm} = 45 \text{ inches} \)[/tex]
6. Calculate the Actual Area in Square Inches:
- Area = Length × Width
- Area = [tex]\( 25 \text{ inches} \times 45 \text{ inches} = 1125 \text{ square inches} \)[/tex]
Hence, the actual area of the space for Joseph's new grill is [tex]\( 1125 \text{ square inches} \)[/tex].
1. Understand the Scale:
- The scale given is 2 cm for every 5 inches.
2. Dimensions of the Grill Space in the Drawing:
- Length in the drawing: 10 cm
- Width in the drawing: 18 cm
3. Convert the Drawing Dimensions to Actual Dimensions:
- First, we need to determine the conversion factor from centimeters to inches, based on the scale.
- For every 2 cm in the drawing, it corresponds to 5 inches in actual size.
4. Conversion Factor Calculation:
- [tex]\( \text{Conversion factor (inches per cm)} = \frac{5 \text{ inches}}{2 \text{ cm}} \)[/tex]
- [tex]\( \text{Conversion factor} = 2.5 \text{ inches per cm} \)[/tex]
5. Convert the Length and Width to Inches:
- Actual length: [tex]\( 10 \text{ cm} \times 2.5 \text{ inches per cm} = 25 \text{ inches} \)[/tex]
- Actual width: [tex]\( 18 \text{ cm} \times 2.5 \text{ inches per cm} = 45 \text{ inches} \)[/tex]
6. Calculate the Actual Area in Square Inches:
- Area = Length × Width
- Area = [tex]\( 25 \text{ inches} \times 45 \text{ inches} = 1125 \text{ square inches} \)[/tex]
Hence, the actual area of the space for Joseph's new grill is [tex]\( 1125 \text{ square inches} \)[/tex].
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