CAT 1994 — QA Question 22
Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 40, 50 and 60 metres. The maximum distance that the fourth could have traveled is (approximately) ….
Answer & solution
Correct answer: Cannot be determined
- A
67 metres
- B
52 metres
- C
22.5 metres
Cannot be determined
Let x and y be the sides of the rectangle ABCD and z
be the length of AP.
Then CR = BP = x – z
By applying Pythagoras Theorem, we have
in Δ APO, a2 =OP2 + z2 ......(i)
in Δ BPO, b2 = OP2 + (x – z)2 ......(ii)
in Δ CRO, d2 = OR2 + (x – z)2 ......(iii)
in Δ DRO, c2 = OR2 + z2 ....... (iv)
Solving above equation, we have a2 + d2 = b2 + c2
∴ For any point inside a rectangle as shown,
a2 + d2 = b2 + c2
∴ Pairing up the distance so that d is to be the maximum,
we get 402 + d2 = 502 + 602
⇒ d = 67 m.