QQuestion
Find the value of 2√3 geometrically.
✓Answer
2√3 = √4×3 = √12
Construction Procedure:
(i) I take two line segments a and b whose lengths are 4 cm and 3 cm respectively.
(ii) From the ray AX, the line segment AB of 4 cm length and from the ray BX, the line segment BC of 3 cm length are cut off.
(iii) I bisect the line segment AC. Let the line segment AC is bisected at the point O. I draw a semicircle by taking the centre at O and the radius of OA or OC length.
(iv) At the point B, I draw a perpendicular on BC which intersects the semicircle at the point D.
∴ BD is mean proportional of the lengths of two line segments AB and BC.
∴ The length of the line segment BD is √12 cm.
By measuring with a scale, I am observing that
BD = 3.5 cm (approx)
∴ √12 = 3.5 (approx)
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