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
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 5 cm
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Understanding |
Application |
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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.
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PQRA is a rectangle: So, QR = AP = 22 cm AR = PQ = 8 cm, BQ = 2 cm and QC = 16 cm RC = QR – QC = 22 – 16 = 6 cm In ΔARC: AC2 = AR2 + RC2 ⇒ AC2 = 82 + 62 ⇒ AC2 = 64 + 36 ⇒ AC = √100 = 10 cm Suppose M and N be the mid – points of AB and AC: So, BN = NC and BM = MA So, MN = AC/2 = 10/2 = 5 cm |
