A rectangle has diagonal 25 cm and breadth (width) 7 cm.\nFind its perimeter in centimetres.

Difficulty: Easy

Correct Answer: 62

Explanation:


Introduction / Context:
For a rectangle with length L and breadth W, the diagonal d satisfies d^2 = L^2 + W^2. From L, W we obtain the perimeter P = 2(L + W). Here d and W are given, so L follows from Pythagoras.


Given Data / Assumptions:

  • d = 25 cm, W = 7 cm.


Concept / Approach:
Compute L = √(d^2 − W^2) and then P = 2(L + W).


Step-by-Step Solution:

L = √(25^2 − 7^2) = √(625 − 49) = √576 = 24 cmPerimeter P = 2(L + W) = 2(24 + 7) = 62 cm


Verification / Alternative check:
Check the triple: 7, 24, 25 is a classic Pythagorean triple. Hence computations are consistent.


Why Other Options Are Wrong:
124 and 82 are double-counting or mixing values; 41 is half of 82 and not a valid perimeter given L and W.


Final Answer:
62

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