Explain two different methods of drawing a line of length centimetres.

(i) As, any odd number, 2k – 1 = k² – (k – 1)²

For,13 = 2k – 1 ⇔ 2k = 14 ⇔ k = 7

So,

√13 = √(7² – 6²)

(units are in c.m.)

Draw a random line and cut a length of 6 c.m. s off it, to have AB.

→ Then draw a normal BA’ on AB.

→ Draw a circular arc with A as the centre and CD as centre, which eventually intersects BA’ at E.

→ Join B and E; and, A and E.

See, In Δ ABE, –

AB⊥ BE

BE² = AE² – AB² = 7² – 6² = 13

óBE = √13 c.m.

(ii) Also observe,

ó

(units are in c.m.)

Draw a random line and cut a length of 3 c.m. off it, to have AB.

→ Then draw a normal BA’ on AB.

→ Draw a circular arc with B as the centre and radius of CD (2 c.m.), which eventually intersects BA’ at E.

→ Join B and E ; and , A and E.

See, In Δ ABE, –

AB⊥ BE

BE² + AB² = AE² = 2² + 3² = 13

óAE = √13