CAT 1997 | Question: 143

Question

In the given figure, $EADF$ is a rectangle and $ABC$ is a triangle whose vertices lie on the sides of $EADF$. $AE = 22,BE = 6,CF = l6$ and $BF = 2$. Find the length of the line joining the midpoints of the sides $AB$ and $BC$.

• A. $4\sqrt{2}$
• B. $5$ 
• C. $3.5$ 
• D. None of these

Answer 1

EF = EB + BF = 6 + 2 = 8

CD = AE - CF = 22 - 16 = 6

BC² = BF² + FC²

=> BC = $\sqrt{260}$

Similarly, AB = $\sqrt{520}$

And AC = 10

By the property of similar triangle, the length of the line joining the midpoints of the sides AB and BC is 5 (Option B)