In This Question All Lengths Are In Centimetres

in this question all lengths are in centimetres

When you encounter a maths or geometry problem that states “in this question all lengths are in centimetres”, the instruction is more than a simple reminder—it sets the stage for every calculation, diagram, and answer you will produce. Recognising why this statement matters, how to apply it consistently, and what pitfalls to avoid can turn a routine exercise into a confidence‑building experience. This article explores the meaning behind the directive, explains its relevance across different topics, and offers a step‑by‑step framework you can use whenever you see it.

Introduction

The phrase in this question all lengths are in centimetres appears frequently in textbooks, exam papers, and online worksheets. Its purpose is to eliminate ambiguity about units so that students can focus on the mathematical relationships rather than worrying about converting between millimetres, metres, or inches. By establishing a single unit of measurement at the outset, the problem becomes a pure exercise in arithmetic, algebra, or geometric reasoning. Understanding how to honour this instruction is essential for scoring full marks and for developing a reliable habit of unit awareness that will serve you in physics, engineering, and everyday life.

Why the Unit Specification Matters

Consistency Prevents Errors

When every length is expressed in the same unit, you avoid the classic mistake of adding centimetres to metres or mixing square centimetres with cubic centimetres. A single unit guarantees that:

• Addition and subtraction are straightforward (no hidden conversion factors).
• Multiplication and division produce results whose units are predictable (e.g., area in cm², volume in cm³).
• Formulas such as (A = \frac{1}{2}bh) or (V = lwh) can be applied directly without extra scaling steps.

Clarity in Communication

Examiners and teachers rely on the unit statement to judge whether a student has interpreted the problem correctly. If you give an answer in metres when the question explicitly demands centimetres, you may lose marks even if the numerical value is correct after conversion. Conversely, stating your answer in centimetres shows that you respected the given constraints.

Building a Habit of Unit Awareness

Treating the instruction as a rule rather than a suggestion trains you to always check units before and after each step. This habit reduces careless errors in more complex, multi‑step problems where unit changes are intentional (e.g., converting speed from km/h to m/s).

Common Problem Types Where the Instruction Appears

Recognising the category helps you select the appropriate formula and anticipate the shape of your answer (linear, squared, or cubed centimetres).

Step‑by‑Step Approach to Solving Problems

Follow this workflow whenever you see the centimetre instruction:

1. Read the entire problem – Highlight the phrase in this question all lengths are in centimetres and any other given numbers.
2. Identify the unknown – Determine what you are asked to find (perimeter, area, volume, angle, etc.).
3. Write down relevant formulas – Keep the unit in mind; for example, area formula yields cm².
4. Substitute the given lengths – Insert the numbers directly; no conversion needed.
5. Carry out the arithmetic – Perform operations step by step, checking each intermediate result for plausibility.
6. Attach the correct unit – Append cm, cm², or cm³ as appropriate.
7. Review – Verify that your answer respects the instruction (i.e., it is expressed in centimetres or its derived unit).

Example Walk‑through

Problem: “A right‑angled triangle has legs measuring 5 cm and 12 cm. In this question all lengths are in centimetres. Find the length of the hypotenuse.”

1. Read – The instruction tells us to treat 5 and 12 as centimetres.
2. Unknown – Hypotenuse (c).
3. Formula – Pythagoras: (c = \sqrt{a^{2}+b^{2}}).
4. Substitute – (c = \sqrt{5^{2}+12^{2}} = \sqrt{25+144}).
5. Calculate – (c = \sqrt{169} = 13).
6. Unit – Since the inputs were centimetres, the hypotenuse is also in centimetres: 13 cm.
7. Review – The answer is a length, correctly expressed in centimetres, satisfying the instruction.

Tips for Maintaining Accuracy

• Write the unit beside every number as you work (e.g., 5 cm, 12 cm). This visual cue prevents accidental dropping of the unit.
• Use a unit column in your rough work: list each quantity with its unit in a separate column; this makes it easy to spot mismatches.
• Check dimensional consistency after each operation: adding two lengths gives a length; multiplying two lengths gives an area; multiplying three lengths gives a volume.
• Avoid premature rounding – keep extra decimal places until the final step, then round to the required precision while still attaching the unit. * Practice with mixed‑unit problems – deliberately convert a few lengths to another unit, solve, then convert back. This reinforces why the single‑unit instruction simplifies the process. ---

Practice Problems (with Solutions) ### Problem 1

Problem1

A rectangular garden measures 8 cm by 15 cm. All dimensions in this exercise are given in centimetres. What is the perimeter of the garden? Solution

1. Identify the required quantity – perimeter of a rectangle. 2. Recall the formula (P = 2(l + w)).
2. Insert the given lengths: (P = 2(8 + 15) = 2 \times 23).
3. Perform the addition and multiplication: (2 \times 23 = 46).
4. Attach the appropriate unit – the result is a length, so the answer is 46 cm.

Problem 2

A cube‑shaped box has each edge measuring 4 cm. All lengths in this question are expressed in centimetres. Compute its surface area.

Solution

1. Surface area of a cube equals (6a^{2}), where (a) is the edge length.
2. Substitute (a = 4): (6 \times 4^{2} = 6 \times 16).
3. Multiply: (6 \times 16 = 96).
4. Since area is measured in square units, the final answer is 96 cm².

Problem 3

A right‑circular cylinder has a radius of 3 cm and a height of 10 cm. All measurements in this problem are in centimetres. Determine the volume of the cylinder.

Solution

1. Volume formula for a cylinder: (V = \pi r^{2}h).
2. Plug in (r = 3) and (h = 10): (V = \pi \times 3^{2} \times 10).
3. Compute the square: (3^{2} = 9). 4. Multiply sequentially: (9 \times 10 = 90); thus (V = 90\pi).
4. Express the result with the proper unit – volume uses cubic units, so the answer is (90\pi) cm³ (approximately 283 cm³ when (\pi) is approximated as 3.14).

Problem 4

A triangle has sides of 7 cm, 24 cm, and 25 cm. All side lengths in this question are given in centimetres. Verify whether the triangle is right‑angled.

Solution

1. For a right‑angled triangle, the Pythagorean relationship must hold: the square of the longest side equals the sum of the squares of the other two.
2. Identify the longest side: 25 cm.
3. Test the equation: (7^{2} + 24^{2} = 49 + 576 = 625).
4. Compare with the square of the longest side: (25^{2} = 625).
5. Since both sides match, the triangle satisfies the condition and is indeed a right‑angled triangle. The verification yields true; no additional unit is required for this logical statement.

Conclusion

Working with a single unit of length simplifies algebraic manipulation and reduces the likelihood of errors. By systematically extracting the relevant data, selecting the appropriate formula, substituting the given values without conversion, and re‑attaching the correct unit at each stage, students can approach a wide variety of geometric tasks with confidence. Practising these steps across different shapes—rectangles, cubes, cylinders, and triangles—reinforces the habit of checking dimensional consistency and ensures that every final answer is both numerically accurate and properly qualified.