Rectangle from diagonal and breadth:\nThe diagonal of a rectangle is 17 cm and its breadth is 8 cm. Find its perimeter (in cm).

Difficulty: Easy

Correct Answer: 46

Explanation:


Introduction / Context:
Given a rectangle’s diagonal and one side, the other side follows from Pythagoras. The perimeter is then twice the sum of the two sides.


Given Data / Assumptions:

  • Diagonal d = 17 cm.
  • Breadth b = 8 cm.


Concept / Approach:
Length l satisfies l^2 + b^2 = d^2. Solve for l, then compute perimeter P = 2(l + b).


Step-by-Step Solution:

l^2 = d^2 − b^2 = 17^2 − 8^2 = 289 − 64 = 225.l = 15 cm.Perimeter P = 2(l + b) = 2*(15 + 8) = 46 cm.


Verification / Alternative check:
Check back: 15^2 + 8^2 = 225 + 64 = 289 = 17^2 (consistent).


Why Other Options Are Wrong:
92 and 84 double something else incorrectly; 42 undercounts.


Common Pitfalls:
Using 2√(l^2 + b^2) as perimeter; that is incorrect—the perimeter is 2(l + b).


Final Answer:
46

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