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

• A.
• B. 5
• C. 3.5
• D. none of these

Answer 1

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${}^{rd}side$)