The diagonal of a rectangle is 17 cm and its breadth is 8 cm. Find the perimeter of the rectangle in centimetres.

Introduction / Context:
This question checks your understanding of how the Pythagoras theorem applies to rectangles. The diagonal of a rectangle acts as the hypotenuse of a right triangle formed by its length and breadth. Once the missing side is computed, calculating the perimeter is straightforward using basic perimeter formulas.

Given Data / Assumptions:

• Diagonal of the rectangle d = 17 cm.
• Breadth b = 8 cm.
• Let length be l cm.
• In a rectangle, diagonal^2 = length^2 + breadth^2.
• Perimeter P = 2 * (l + b).

Concept / Approach:
Use the Pythagoras theorem on the right triangle formed by the length, breadth, and diagonal. Knowing two sides (breadth and diagonal), you can solve for the third side (length). Then substitute length and breadth into the perimeter formula to find the total boundary length of the rectangle.

Step-by-Step Solution:
Given diagonal d = 17 cm and breadth b = 8 cm. Use the relation d^2 = l^2 + b^2. So 17^2 = l^2 + 8^2. 289 = l^2 + 64. l^2 = 289 - 64 = 225. l = square root of 225 = 15 cm. Now find perimeter P = 2 * (l + b) = 2 * (15 + 8) = 2 * 23 = 46 cm.

Verification / Alternative check:
You may quickly verify by checking the Pythagoras triple 8, 15, 17. Since 8^2 + 15^2 = 64 + 225 = 289 and 17^2 = 289, this matches exactly, confirming that the right triangle assumption is correct. So length 15 cm and breadth 8 cm give a consistent rectangle with diagonal 17 cm and perimeter 46 cm.

Why Other Options Are Wrong:
92 and 84: These correspond to larger perimeters that would require larger side lengths than those allowed by the diagonal. 42 and 34: These correspond to smaller perimeters and would not match a diagonal of 17 cm when using the Pythagoras theorem.

Common Pitfalls:
Forgetting to square the given diagonal and breadth when applying the Pythagoras theorem. Using perimeter formula incorrectly, such as l + b instead of 2 * (l + b). Making arithmetic mistakes in subtracting 64 from 289 or in taking the square root of 225.

Final Answer:
The perimeter of the rectangle is 46 cm