Q.3. Show how 5 can be represented on the number line.

Solution:

We can write 5 = 4 + 1 = (2)2 + (1)2

So we will construct a right angled triangle with sides 2 and 1 and the hypotenuse will be the required measure of 5.

  1. Let AB be a line of length 2 unit on number line.

  2. At B, draw a perpendicular line BC of length 1 unit. Join CA.

  3. Now, ABC is a right angled triangle.

    Applying Pythagoras theorem,

    AB2 + BC2 = CA2

    ⇒ 22 + 12 = CA2

    ⇒ CA2 = 5

    ⇒ CA = 5

    Thus, CA is a line of length 5 unit.


  4. Taking CA as a radius and A as a centre draw an arc cutting the number line at D. Now AD = AC = 5, because they are the radii of the same circle.

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