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

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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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

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1

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?

2

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:
    (28×10)=280 square meters(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:
    (84×30)=2520 square meters(84 \times 30) = 2520 \text{ square meters}.
  • Step 3: Find the ratio of the new classroom's area to the original classroom's area:
    2520280=9\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:
    9×3799=341919 \times 3799 = 34191.

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

3

Final Answer

34191

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