CAT 1997 — QA Question 43
Direction: Answer the questions based on the following information.
Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.
In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC.
Answer & solution
- A
4√2
5
- C
3.5
- D
None of these
We know that length of the line joining the mid-points of two sides of a triangle is half the length of third side. Hence, the required length is half the length of side AC. Since EADF is rectangle, EF = AD = 8.
CD = (22 – 16) = 6.
So in the right-angled ΔADC, AD = 8 and CD = 6.
Therefore, AC = 10. Hence, length of the line joining the mid-points of AB and BC = (10) = 5.