-
PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ∆ ABC 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
-
- 4√2 cm.
- 5 cm.
- 6 cm.
- 10 cm.
- 4√2 cm.
Correct Option: B
On the basis of question we draw a figure of rectangle PQRA and ABC is a triangle whose vertices lie on the sides of PQRA ,
Given that , QR = AP = 22 cm, PQ = 8 cm BQ = 2 cm and QC = 16 cm.
∴ CR = QR - QC = 22 – 16 = 6 cm.
BC = √BQ² + QC²
BC = √2² + 16²
BC = √4 + 256
BC = √260 cm.
AC = √CR² + AR²
AC = √6² + 8²
AC = √36 + 64
AC = √100 = 10 cm.
BD = DC
BE = EA
| ∴ DE || AC and DE = | AC | |
| 2 |
DE = 10 ÷ 2 = 5 cm.
