The diagram shows a scale drawing of a playground in the scale drawing the playground has a length of 16 centimeters and a width of 8 centimeters the area of the actual playground is 72nsquare meters what is the scale of the drawing

Answer 1

To find the scale of the drawing, we first need to determine the area of the scale drawing and compare it to the actual area of the playground.

1. Calculate the area of the scale drawing: \[ \text{Area of the scale drawing} = \text{length} \times \text{width} = 16 , \text{cm} \times 8 , \text{cm} = 128 , \text{cm}^2 \]

2. Convert the area of the actual playground to square centimeters: Since 1 square meter is equal to \(10,000\) square centimeters, we convert \(72 , \text{m}^2\) to square centimeters: \[ \text{Area of the actual playground} = 72 , \text{m}^2 \times 10,000 , \text{cm}^2/\text{m}^2 = 720,000 , \text{cm}^2 \]

3. Find the scale of the drawing: The scale can be determined by comparing the dimensions of the scale drawing to the actual dimensions. We need to find the length and width of the actual playground.

   The dimensions of the actual playground can be calculated using the area: \[ \text{Area} = \text{length} \times \text{width} \]

   We know the area is \(720,000 , \text{cm}^2\). Assuming the length-to-width ratio is the same as in the scale drawing, we can set up a ratio:

   \[ \frac{\text{length}}{\text{width}} = \frac{16}{8} = 2 \]

   Let \(w\) be the actual width. Then the actual length \(l\) is: \[ l = 2w \]

   Substitute this into the area equation: \[ l \times w = 720,000 \] \[ (2w) \times w = 720,000 \] \[ 2w^2 = 720,000 \] \[ w^2 = 360,000 \] \[ w = \sqrt{360,000} \approx 600 , \text{cm} \] This makes the actual length: \[ l = 2(600) = 1200 , \text{cm} \]

4. Determine the scale: Now we have:

   • Scale drawing dimensions: \(16 , \text{cm} \times 8 , \text{cm}\)
   • Actual playground dimensions: \(1200 , \text{cm} \times 600 , \text{cm}\)

   The scale for each dimension is: \[ \frac{\text{scale drawing length}}{\text{actual length}} = \frac{16 , \text{cm}}{1200 , \text{cm}} = \frac{1}{75} \] \[ \frac{\text{scale drawing width}}{\text{actual width}} = \frac{8 , \text{cm}}{600 , \text{cm}} = \frac{1}{75} \]

Therefore, the scale of the drawing is 1:75.

Answer 2

U sure

Answer 3

Let's carefully verify the calculations step by step to ensure accuracy regarding the scale of the playground drawing.

1. Area of the Scale Drawing:

   • Length = 16 cm
   • Width = 8 cm \[ \text{Area of the Scale Drawing} = \text{Length} \times \text{Width} = 16 , \text{cm} \times 8 , \text{cm} = 128 , \text{cm}^2 \]

2. Actual Area of the Playground:

   • The area of the actual playground is given as 72 square meters.
   • Convert this to square centimeters: \[ \text{Area of Actual Playground} = 72 , \text{m}^2 \times 10,000 , \text{cm}^2/\text{m}^2 = 720,000 , \text{cm}^2 \]

3. Finding the Actual Dimensions: Assuming the actual playground maintains the same length-to-width ratio as the scale drawing (which is 2:1 since \(16:8 = 2:1\)), we can express the actual dimensions in terms of width \(w\):

   • Let \(w\) be the actual width, then the actual length \(l = 2w\).
   • Set up the area equation: \[ l \times w = 720,000 , \text{cm}^2 \] Substituting for \(l\): \[ (2w) \times w = 720,000 \] \[ 2w^2 = 720,000 \] \[ w^2 = 360,000 \] \[ w = \sqrt{360,000} \approx 600 , \text{cm} \] Therefore, the actual length: \[ l = 2w = 2(600) = 1200 , \text{cm} \]

4. Calculating the Scale: Now we find the scale by comparing the dimensions of the actual playground to those of the scale drawing:

   • Scale drawing dimensions: \(16 , \text{cm} \times 8 , \text{cm}\)
   • Actual playground dimensions: \(1200 , \text{cm} \times 600 , \text{cm}\)

   Calculate the Scale Ratio: \[ \text{Scale for length} = \frac{\text{Scale Drawing Length}}{\text{Actual Length}} = \frac{16 , \text{cm}}{1200 , \text{cm}} = \frac{1}{75} \] \[ \text{Scale for width} = \frac{\text{Scale Drawing Width}}{\text{Actual Width}} = \frac{8 , \text{cm}}{600 , \text{cm}} = \frac{1}{75} \]

Thus, the final scale of the drawing remains consistent and is indeed 1:75. Your inquiry prompted a thorough check, and I can confirm the calculations are correct. Thank you for prompting the verification!

Answer 4

N that’s wrong

Answer 5

I apologize for any confusion. Let's go through the calculation again step by step to ensure we get the correct scale.

Given:

• Length of the scale drawing: 16 cm
• Width of the scale drawing: 8 cm
• Area of the actual playground: 72 m²

Step 1: Convert the Area of the Actual Playground

First, we need to convert the actual area from square meters to square centimeters.

1 m² = 10,000 cm²

So: \[ 72 , \text{m}^2 = 72 \times 10,000 = 720,000 , \text{cm}^2 \]

Step 2: Calculate the Area of the Scale Drawing

Calculate the area of the scale drawing: \[ \text{Area of the scale drawing} = \text{Length} \times \text{Width} = 16 , \text{cm} \times 8 , \text{cm} = 128 , \text{cm}^2 \]

Step 3: Finding the Scale in Terms of Area

Now, our next step is to calculate the scale in terms of the area of the actual playground compared to the area of the scale drawing.

Ratio of Areas: \[ \text{Scale factor in area} = \frac{\text{Area of actual playground}}{\text{Area of scale drawing}} = \frac{720,000 , \text{cm}^2}{128 , \text{cm}^2} \]

Calculating this gives: \[ \frac{720,000}{128} = 5625 \]

Step 4: Finding the Linear Scale

The area scale factor is the square of the linear scale factor. Therefore, to find the linear scale factor, we take the square root of the area scale: \[ \text{Linear scale factor} = \sqrt{5625} = 75 \]

Step 5: Final Scale

Thus the scale of the drawing is: \[ 1:75 \]

Conclusion

It seems that the earlier calculation of the scale being 1:75 was indeed correct when considering both dimensions. If you have additional information or specifics that are leading to a different conclusion or if there are particular premises I might have misunderstood, please let me know. I’m here to help clarify!

Answer 6

Is it 9 cm:16m
3cm:4m
4 cm:3m
16cm:9m

Answer 7

Let's go through the problem based on the options you've provided for the scale representation of the playground to address your question accurately.

Given:

1. Length of the scale drawing: 16 cm
2. Width of the scale drawing: 8 cm
3. Area of the actual playground: 72 m²

Step 1: Convert the Area

Convert the area of the playground to square centimeters since the scale drawing dimensions are in centimeters: \[ 72 , \text{m}^2 = 72 \times 10,000 = 720,000 , \text{cm}^2 \]

Step 2: Find the Scale Ratio

Now, we want to find the scale in linear terms. The ratio of the areas indicates that we will find the linear scale based on the dimensions of the actual playground.

Step 3: Assuming the Actual Dimensions

Since the drawing is in a length-to-width ratio of 2:1 (length/width = 16/8 = 2), let’s denote:

• Actual Width (w) = x m
• Actual Length (l) = 2x m

The area of the actual playground can then be expressed as: \[ (2x) \cdot x = 72 \implies 2x^2 = 72 \implies x^2 = 36 \implies x = 6 , \text{m} \]

So,

• Actual Width = \(6 , \text{m}\)
• Actual Length = \(2 \cdot 6 , \text{m} = 12 , \text{m}\)

Step 4: Find the Scale

Now, determine the scale in terms of these actual dimensions.

To find the scale:

• Actual Length: 12 m corresponds to 16 cm
• Actual Width: 6 m corresponds to 8 cm

We can write the scale in terms of width: \[ \text{Width Scale: } \frac{8 , \text{cm}}{6 , \text{m}} \left( \frac{1 , \text{m}}{100 , \text{cm}} \right) = \frac{8}{600} = \frac{2}{150} \approx \frac{1}{75} \]

However, to express this in a straightforward ratio, we can consider how each dimension relates to a certain number of centimeters:

1. Conversions
   • 8 cm to 6 m (600 cm): 8 cm : 600 cm → \( \frac{8}{600} = \frac{1}{75} \)
   • 16 cm to 12 m (1200 cm): 16 cm : 1200 cm → \( \frac{16}{1200} = \frac{1}{75} \)

As both dimensions yield the consistent conversion to a scale ratio of 1:75, we can directly look at your options:

Reviewing Your Options:

Now, let’s analyze your potential scale ratios:

1. 9 cm:16 m = \( \frac{9}{1600} \) (Not equivalent to 1:75)
2. 3 cm:4 m = \( \frac{3}{400} \) (Not equivalent to 1:75)
3. 4 cm:3 m = \( \frac{4}{300} \) (Not equivalent to 1:75)
4. 16 cm:9 m = \( \frac{16/900} \) (Not equivalent to 1:75)

Scale Representation and Final Answer

Each of these ratios does not exactly represent the same scale relationship as established with the area and dimension conversions.

From the verified dimensions:

• The correct simplified scale based on the drawing and actual size is indeed 1:75.

Make sure to re-evaluate the 9 cm:16 m, 3 cm:4 m, 4 cm:3 m, and 16 cm:9 m ratios compared to 1:75. The correct choice that matches the scaling between the areas and their dimensions based on the initial provided area is 1:75, which corresponds closely to 16 cm:12 m if we relate specific lengths (though 3 cm:4 m might simplify ratios but doesn’t derive from the area calculation).

If the options you’re seeking are alternatives derived from comparing actual measurements or scales, further context on how you’re interpreting those ratios might help refine the right selection. Kindly check and feel free to clarify for further assistance!