Rectangular Garden Bed Measurements

00:00 6 marks

A rectangular garden bed has length \(l\) = 5.8 m and width \(w\) = 2.4 m, both measured correct to the nearest 0.1 metre.

(a) Write down the interval within which the true length \(l\) lies. [1]

(b) Calculate the lower bound for the perimeter of the garden bed. [2]

(c) Calculate the percentage error in using the measured values to calculate the area of the garden bed, compared to the minimum possible area. [3]

Part a

3 minutes 1 marks

Question

Write down the interval within which the true length \(l\) lies.

Hint Hint

Hint

Since the measurement is correct to the nearest 0.1 m, adjust \(l = 5.8\) m by ±0.05 m to get the interval.

Answer Answer
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Explanation Explanation

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Complete Answer

The interval is [5.75, 5.85) m.

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Part b

3 minutes 2 marks

Question

Calculate the lower bound for the perimeter of the garden bed.

Hint Hint

Hint

Use the lower bounds for the length and the width in the formula for perimeter: 2(l + w).

Answer Answer
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Explanation Explanation

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Complete Answer

Lower bound perimeter = 2(5.75 + 2.35) = 16.2 m

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Part c

4 minutes 3 marks

Question

Calculate the percentage error in using the measured values to calculate the area of the garden bed, compared to the minimum possible area.

Hint Hint

Hint

First compute the measured area and the minimum area using the lower bounds. Then, calculate the percentage error as |(measured area – minimum area) / minimum area| × 100.

Answer Answer
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Explanation Explanation

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Complete Answer

Percentage error ≈ 3.02%

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