Q. 3

We have seen in Class 7 that any odd number can be written as the difference of two perfect squares. (The lesson, Identities) Usingthis, draw lines of lengths centimetres.

Answer :

Any odd number can be written in the form 2k – 1,k being a natural number.


Now,2k – 1 = k2 – (k – 1)2


● For,


2k – 1 = 7


2k = 8


k = 4


So, √7 = 42 – 32


So, if we draw a line of 4 units, say CD, then,



Then,



Draw a random line and cut a length of 3c.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 = 42 – 32 = 7


E = √7 c.m.


● And,


2k – 1 = 11


2k = 12


k = 6


So, √11 = √( 62 – 52)


Draw a random line and cut a length of 5 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 = 62 – 52 = 11


óBE = √11 c.m.



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