An estimate of the height, H meters, of a tall building can be found using the formula H = 4f+12 where the building is F floor high. A tall building is 110 floors high. The real height of the building is 442m. Seb uses the formula to find the estimate of the height of this building. He then find the difference between his estimate and the real height. Shoe that the difference is less than 5% of the real height. Find what the percentage the difference is of the real height and enter this value correct to 1 decimal place

Given:
- Formula to estimate the height: \( H = 4F + 12 \), where \( F \) is the number of floors.
- The building has \( F = 110 \) floors.
- Real height of the building = 442 meters.

### Step 1: Calculate the Estimated Height
Using the formula \( H = 4F + 12 \):

\[
H = 4 \times 110 + 12 = 440 + 12 = 452 \, \text{meters}.
\]

### Step 2: Find the Difference Between the Estimated and Real Height
The difference is:

\[
\text{Difference} = 452 - 442 = 10 \, \text{meters}.
\]

### Step 3: Calculate the Percentage of the Difference with Respect to the Real Height
The percentage difference is given by:

\[
\text{Percentage difference} = \left( \frac{\text{Difference}}{\text{Real height}} \right) \times 100 = \left( \frac{10}{442} \right) \times 100.
\]

Let's calculate this:

\[
\text{Percentage difference} \approx \left( \frac{10}{442} \right) \times 100 \approx 2.26\%.
\]

Rounding this to 1 decimal place gives:

\[
\text{Percentage difference} = 2.3\%.
\]

Since 2.3% is less than 5%, Seb's estimate is indeed within the required range.

### Final Answer
The percentage difference is **2.3%**.

Would you like further explanation or have any questions?

### Related Questions
1. How would the formula change if the additional height per floor varied?
2. What would the estimated height be for a building with 200 floors using the same formula?
3. How sensitive is the percentage difference to changes in the number of floors?
4. What real-life factors could cause a difference between estimated and real building heights?
5. If a building's actual height is underestimated by 3%, how many meters would that be for a 600-meter tall building?

### Tip
Always double-check percentage calculations by ensuring the ratio is taken relative to the correct "whole" (in this case, the real height).

An estimate of the height, H meters, of a tall building can be found using the formula H = 4F + 12 where the building is F floors high. A tall building is 110 floors high. The real height of the building is 442m. Seb uses the formula to find the estimate of the height of this building. He then finds the difference between his estimate and the real height. Show that the difference is less than 5% of the real height. Find what percentage the difference is of the real height and enter this value correct to 1 decimal place.

Learn how to calculate the percentage difference between an estimated and real building height using the formula H = 4F + 12. For a building with 110 floors and a real height of 442 meters, this problem demonstrates how to verify that the difference is less than 5%. Ideal for students in Grades 7-9.

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