By geometrical construction, it is possible to divide a line segment in the ratio 2 + √3: 2 - √3. Write ‘True’ or ‘False’ and justify your answer

Solution:

From the question,

Ratio = 2 + √3 : 2 - √3

On further simplification

(2 + √3)/ (2 - √3)

Multiply and divide by (2 + √3)

= (2 + √3)/ (2 - √3) × (2 + √3)/(2 + √3)

By further calculation

= (4 + 2√3 + 2√3 + 3)/ (4 - 3)

So we get

= (7 + 4√3)/ 1

(7 + 4√3) : 1

Here (7 + 4√3) is not a positive integer where 1 is a positive integer.

Therefore, the statement is false.

✦ Try This: By geometrical construction, it is possible to divide a line segment in the ratio 4 + √5: 4 - √5.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11

NCERT Exemplar Class 10 Maths Exercise 10.2 Sample Problem 1

By geometrical construction, it is possible to divide a line segment in the ratio 2 + √3: 2 - √3. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “By geometrical construction, it is possible to divide a line segment in the ratio 2 + √3: 2 - √3” is false

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