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

Answer 1

The correct option is B 5

EF = AD = 8 ($\therefore$ 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 $=\frac{1}{2}\left(10\right)=5$
($\because$ The length of the line joining the mid-point of the two sides of triangle is half the 3rd)