In a rectangle, the length of the diagonal is 17 centimetres and the breadth is 8 centimetres. Find the perimeter of the rectangle in centimetres.

Introduction / Context:
This aptitude question tests your understanding of the relationship between the sides and the diagonal of a rectangle, and how to use that relationship to find the perimeter. Such questions are very common in competitive exams and help reinforce concepts from coordinate and Euclidean geometry.

Given Data / Assumptions:

• The figure is a rectangle.
• The diagonal of the rectangle is 17 cm.
• The breadth (shorter side) of the rectangle is 8 cm.
• We must find the perimeter of the rectangle in centimetres.
• The rectangle has opposite sides equal and all angles are 90 degrees.

Concept / Approach:
In a rectangle, the diagonal, length, and breadth form a right angled triangle. Therefore, we can apply the Pythagoras theorem:
length^2 + breadth^2 = diagonal^2.
Once we find the length, we use the formula for the perimeter of a rectangle:
Perimeter = 2 * (length + breadth).

Step-by-Step Solution:
Step 1: Let the length of the rectangle be L cm and breadth be B = 8 cm. Step 2: The diagonal D = 17 cm. By Pythagoras theorem: L^2 + B^2 = D^2. Step 3: Substitute values: L^2 + 8^2 = 17^2. Step 4: Compute squares: L^2 + 64 = 289. Step 5: Rearrange: L^2 = 289 - 64 = 225. Step 6: Take square root: L = 15 cm (length is positive). Step 7: Now compute perimeter: Perimeter = 2 * (L + B) = 2 * (15 + 8). Step 8: Perimeter = 2 * 23 = 46 cm.

Verification / Alternative check:
We can quickly verify by rechecking the diagonal:
15^2 + 8^2 = 225 + 64 = 289, and 17^2 = 289, so the diagonal value is consistent. Therefore the dimensions are correct, and the perimeter must be 46 cm.

Why Other Options Are Wrong:
42 cm: This would correspond to 21 cm total for length plus breadth, which is not correct for the given diagonal.
50 cm: This implies a different combination of length and breadth that does not give a diagonal of 17 cm.
84 cm: Much too large and does not match the computed side lengths.
92 cm: Exactly double of 46 cm and clearly not appropriate for this rectangle.

Common Pitfalls:
Students sometimes confuse the formula for the perimeter with that for the area. Another common error is to forget to apply the Pythagoras theorem correctly or to make mistakes in squaring or square root computation. Some also mistakenly double only one side rather than doubling the sum of both sides when calculating the perimeter.

Final Answer:
The perimeter of the rectangle is 46 cm.