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Question
The mean proportional of the line segments of length 3 cm and 6 cm is ___ (Use geometric method).
The mean proportional of the line segments of length 3 cm and 6 cm is
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Solution
The correct option is B 4.2 cm
Steps of Construction:
i) Draw a ray AX of length greater than (6 + 3) cm.
ii) Cut off the part AB from AX equal to 6 cm and the part BC from BX equal to 3 cm.
iii) Draw a perpendicular bisector PQ of AC. PQ intersects AC at O.
iv) Draw a semi circle by taking centre at O and radius equal to OA or OC.
v) Draw a perpendicular on OC at B, which intersects the semi circle at the point D.
vi) Join B and D.
vii) BD is the required mean proportional.
BD is equal to 4.2 cm.
Hence, the mean proportional = 4.2 cm.
4.2 cm
Steps of Construction:
i) Draw a ray AX of length greater than (6 + 3) cm.
ii) Cut off the part AB from AX equal to 6 cm and the part BC from BX equal to 3 cm.
iii) Draw a perpendicular bisector PQ of AC. PQ intersects AC at O.
iv) Draw a semi circle by taking centre at O and radius equal to OA or OC.
v) Draw a perpendicular on OC at B, which intersects the semi circle at the point D.
vi) Join B and D.
vii) BD is the required mean proportional.
BD is equal to 4.2 cm.
Hence, the mean proportional = 4.2 cm.
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