Question

Find the value of $\sqrt{20}$ using geometric method.

• A. 5.1
• B. 3
• C. 3.9
• D. 4.5

Answer 1

The correct option is D

4.5

We know that $20=5\times 4$

So, we can construct the mean proportional of two line segments of lengths 5 cm and 4 cm, which will be the required square root of 20.

Method of Construction:

Let us consider the two numbers as a and b where a = 5 cm, b = 4 cm.

(i) Let us draw a ray AX of length greater than (a + b) = (5 + 4) = 9 cm.

(ii) Let us cut off the part AB from AX equal to a cm (5 cm) and the part BC from BX equal to b cm (4 cm)

(iii) Let us draw perpendicular bisector PQ of AC. Let PQ intersect AC at O.

(iv) Let us draw a semi circle by taking centre at O and radius equal to OA or OC.

(v) Let us now draw a perpendicular an OC at B, which Intersects the semi circle at the point D.

(vi) Let us join B & D.

Here, AB = 5 cm, BC = 4 cm. BD is the required mean proportional of AB and BC. By scale, BD = 4.5 cm (approx) = $\sqrt{20}$