PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ΔABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm. Then the length of the line joining the mid points of the sides AB and BC is.

Solution (By Examveda Team)

Given that AP = 22 cm and PQ = 8 cm

Made a triangle such that B, is on side PQ and BQ = 2 cm
And C is on RQ such that QC = 16 cm
Because all the vertices are on sides of PQRA.
Now, PQRA is a rectangle so all the angle will be of 90°.
∠ARQ = 90°
and RC = RQ - CQ = 22 - 16 cm = 6 cm
In right angle ΔARC
AC² = AR² + RC² = 8² + 6²
$$\boxed{{\text{AC}} = 10}$$
Now in ΔABC, AC is 10 cm and M, N are the mid point of ΔABC.
So, MN = $$\frac{{10}}{2}$$ = 5 cm