Calculate Flooring Cost: Scaling from 28x10m to 84x30m Room

Q: Why do I multiply the dimensions instead of adding them?

You need area (space to cover with flooring), not perimeter (distance around edges). Area = length × width gives you square meters. Adding gives you the distance around the room's border.

Q: How do I know the cost scales with area?

Flooring cost depends on how much material you need. More area = more wood planks = higher cost. If the area doubles, the cost doubles too - this is proportional reasoning.

Q: Can I just multiply the original cost by the ratio of dimensions?

No! You must use the area ratio, not dimension ratios. The room is 3 times longer (84÷28) and 3 times wider (30÷10), but the area is 3×3 = 9 times larger.

Q: What if the areas don't divide evenly?

Use a calculator for the division and keep enough decimal places for accuracy. Then multiply by the original cost. Round your final answer to the nearest whole currency unit.

Q: How can I check my area calculations are right?

Double-check by calculating each area separately: 280 = 28 × 10 and 2520 = 84 × 30. Then verify the ratio: $ \frac{2520}{280} = 9 $.

Area Scaling with Proportional Reasoning

A school paid 3799 to install a wood floor in the classroom of 28 mts by 10 mts. How much does it cost to install a wood floor in a similar room with dimensions of 84 mts and 30 mts?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How much will we pay for tiling rectangle 2?

00:03 Similar rectangles according to the given data

00:08 Let's find the similarity ratio

00:14 The area ratio equals the similarity ratio squared

00:22 This is the area ratio

00:33 We'll multiply this ratio by the original payment

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A school paid 3799 to install a wood floor in the classroom of 28 mts by 10 mts. How much does it cost to install a wood floor in a similar room with dimensions of 84 mts and 30 mts?

Step-by-step solution

To solve this problem, we’ll perform the following steps:

Step 1: Calculate the area of the original classroom:
Since the dimensions are given as 28 mts by 10 mts, the area is:
$(28 \times 10) = 280 \text{ square meters}$ .
Step 2: Calculate the area of the new classroom:
The dimensions are given as 84 mts by 30 mts, so the area is:
$(84 \times 30) = 2520 \text{ square meters}$ .
Step 3: Find the ratio of the new classroom's area to the original classroom's area:
$\frac{2520}{280} = 9$ .
Step 4: Calculate the cost for the new classroom:
Since the area is 9 times larger, the cost will be 9 times the original cost:
$9 \times 3799 = 34191$ .

Therefore, the cost to install a wood floor in the new classroom is $34191$ .

Final Answer

34191

Key Points to Remember

Essential concepts to master this topic

Area Formula: Multiply length by width to find square meters
Scaling Technique: New area ÷ original area = cost multiplier (2520 ÷ 280 = 9)
Verification: Check that 9 × 3799 = 34191 and areas are calculated correctly ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying for area
Don't calculate area as 28 + 10 = 38 and 84 + 30 = 114 = wrong areas! Adding gives perimeter, not area, leading to completely incorrect cost calculations. Always multiply length × width to find area in square units.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I multiply the dimensions instead of adding them?

You need area (space to cover with flooring), not perimeter (distance around edges). Area = length × width gives you square meters. Adding gives you the distance around the room's border.

How do I know the cost scales with area?

Flooring cost depends on how much material you need. More area = more wood planks = higher cost. If the area doubles, the cost doubles too - this is proportional reasoning.

Can I just multiply the original cost by the ratio of dimensions?

No! You must use the area ratio, not dimension ratios. The room is 3 times longer (84÷28) and 3 times wider (30÷10), but the area is 3×3 = 9 times larger.

What if the areas don't divide evenly?

Use a calculator for the division and keep enough decimal places for accuracy. Then multiply by the original cost. Round your final answer to the nearest whole currency unit.

How can I check my area calculations are right?

Double-check by calculating each area separately: 280 = 28 × 10 and 2520 = 84 × 30. Then verify the ratio: $\frac{2520}{280} = 9$ .

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