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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 = 16 and BF = 2. Find the length of the line joining the mid-point of the sides AB and BC.

A
42
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B
5
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C
3.5
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D
None of these
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Solution

The correct option is B 5
EF = AD = 8 ( EADF is a rectangle)

CD = (22 - 16) = 6
So, in the right-angled triangle ADC, AD = 8 and CD = 6
AC = 10
Length of the line joining the mid-points of AB and BC =12(10)=5
( The length of the line joining the mid-point of the two sides of triangle is half the 3rd)

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