The area of a rectangle is 120 square centimetres and its breadth is 8 centimetres. What must be the length of the diagonal of this rectangle, in centimetres?

Introduction / Context:
This problem combines two basic properties of rectangles. First, the area of a rectangle is the product of its length and breadth. Second, the diagonal of a rectangle can be obtained by applying the Pythagoras theorem to the length and breadth. Such questions are standard in aptitude tests and help you practise linking area with side lengths and diagonals.

Given Data / Assumptions:
- Area of the rectangle = 120 square centimetres.
- Breadth (one side) = 8 centimetres.
- The rectangle has right angles at each corner by definition.
- We need to find the length of the diagonal in centimetres.

Concept / Approach:
The area A of a rectangle is given by:
A = length * breadth
So we can find the length by dividing the area by the breadth. Once we know length and breadth, we use the Pythagoras theorem because the diagonal forms the hypotenuse of a right angled triangle with the length and breadth as legs. Thus:
diagonal^2 = length^2 + breadth^2
and diagonal is the positive square root of this sum.

Step-by-Step Solution:
Step 1: Use the area formula A = length * breadth. Step 2: Substitute A = 120 and breadth = 8. So 120 = length * 8. Step 3: Solve for length: length = 120 / 8 = 15 cm. Step 4: Apply Pythagoras theorem to find the diagonal d: d^2 = length^2 + breadth^2. Step 5: Compute d^2 = 15^2 + 8^2 = 225 + 64 = 289, so d = √289 = 17 cm.

Verification / Alternative check:
As a quick check, note that the triple (8, 15, 17) is a well known Pythagorean triple where 8^2 + 15^2 = 17^2. Therefore, a rectangle with sides 8 cm and 15 cm will always have a diagonal of 17 cm. This gives additional confidence that the answer is correct.

Why Other Options Are Wrong:
30 cm and 34 cm are much larger than the sum of the sides and would make the Pythagoras relation invalid because 15^2 + 8^2 does not equal 30^2 or 34^2.
15 cm is simply the length of the rectangle, not the diagonal, so it ignores the breadth.
25 cm also fails the Pythagoras check because 15^2 + 8^2 is not equal to 25^2.

Common Pitfalls:
Some learners forget to find the length first and try to guess or use incorrect formulas for the diagonal. Others mistakenly add the sides rather than adding the squares of the sides. Always remember that the diagonal of a rectangle is obtained using the Pythagoras theorem, not by simple addition of length and breadth.

Final Answer:
The length of the diagonal of the rectangle is 17 cm.