In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE =16, CF = 16, CF = 16 and BF = 2. Find the length of the line joining the
mid-points of the sides AB and BC.
(CAT 1997)

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3.5

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Solution

The correct option is B 5
Option (b)

EF = AD = 8

(EADF is a rectangle)

CD = (22 – 16) = 6

So in the right angled triangle ADC, AD = 8 and CD = 6.

Therefore AC = 10

Therefore length of the line joining the mid – points of

AB and BC = $\frac{1}{2}$ (10) = 5

(length of the line joining the mid – point of two sides of a triangle is half the 3$^{rd}$

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In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE =16, CF = 16, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC. (CAT 1997)

In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE =16, CF = 16, CF = 16 and BF = 2. Find the length of the line joining the
mid-points of the sides AB and BC.
(CAT 1997)