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A and B are standing at either ends of the diagonal of a rectangular room. B starts walking along the diagonal to reach the other end of the diagonal. A walk along the length and breadth to reach the other end of the diagonal. A takes 7 seconds to travel which is 2 seconds more than the time taken by B. B travelled 20 m. Find the perimeter of the room, given that speed of A and B is same.

A and B are standing at either ends of the diagonal of a rectangular room. B starts walking along the diagonal to reach the other end of the diagonal. A walk along the length and breadth to reach the other end of the diagonal. A takes 7 seconds to travel which is 2 seconds more than the time taken by B. B travelled 20 m. Find the perimeter of the room, given that speed of A and B is same. Correct Answer 56 m

Given:

A and B are standing at either ends of the diagonal of a rectangular room. B starts walking along the diagonal to reach the other end of the diagonal. A walk along the length and breadth to reach the other end of the diagonal. A takes 7 seconds to travel which is 2 seconds more than the time taken by B. B travelled 20 m.

Formula:

Distance = speed × time

Calculation:

Let the length and breadth of the rectangular room be l and b respectively.

B took 5 seconds.

⇒ Speed of B = 20/5 = 4 m/s

Speed of A = 4m/s

Distance A travelled = 4 × 7 = 28 m

Distance B travelled = 20 m

⇒ l + b = 28

⇒ l2 + b2 = 202

⇒ l2 + (28 – l)2 = 20

⇒ l = 16 and b = 12

∴ required perimeter = 2 × (l + b) = 2 × (16 + 12) = 2 × 28 = 56 m

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