Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length 7.3 cm and $¯ ¯¯¯¯¯¯¯ ¯ C D$ of length 3.4 cm, construct a line segment $¯ ¯¯¯¯¯¯¯ ¯ X Y$ such that the length of $¯ ¯¯¯¯¯¯¯ ¯ X Y$ is equal to the difference between the lengths of $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ . Verify by measurement

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Solution

Steps of construction:
(i) Draw a line 'l' and take a point X on it.
(ii) Construct $¯ ¯¯¯¯¯¯¯ ¯ X Z$ such that length $¯ ¯¯¯¯¯¯¯ ¯ X Z$ = length of $¯ ¯¯¯¯¯¯ ¯ A B$ = 7.3 cm
(iii) Then cut off $¯ ¯¯¯¯¯¯ ¯ Z Y$ = length of $¯ ¯¯¯¯¯¯¯ ¯ C D$ = 3.4 cm
(iv) Thus the length of $¯ ¯¯¯¯¯¯¯ ¯ X Y$ = length of $¯ ¯¯¯¯¯¯ ¯ A B$ – length of $¯ ¯¯¯¯¯¯¯ ¯ C D$

Verification:

Hence, by measurement we find that length of $¯ ¯¯¯¯¯¯¯ ¯ X Y$ = 3.9 cm
= 7.3 cm – 3.4 cm
= $¯ ¯¯¯¯¯¯ ¯ A B$ - $¯ ¯¯¯¯¯¯¯ ¯ C D$

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Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length $7.3 c m$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ of length $3.4 c m$ , construct a line segment $¯ ¯¯¯¯¯¯¯ ¯ X Y$ such that the length of $¯ ¯¯¯¯¯¯¯ ¯ X Y$ is equal to the difference between the lengths of $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ . Verify by measurement

Question 4

Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length 3.9 cm, construct $¯ ¯¯¯¯¯¯ ¯ P Q$ such that the length $¯ ¯¯¯¯¯¯ ¯ P Q$ is twice that of AB . Verify by measurement.

(Hint: Construct $¯ ¯¯¯¯¯¯¯ ¯ P X$ such that length of $¯ ¯¯¯¯¯¯¯ ¯ P X$ = length of $¯ ¯¯¯¯¯¯ ¯ A B$ ;
then cut off $¯ ¯¯¯¯¯¯¯ ¯ X Q$ such that $¯ ¯¯¯¯¯¯¯ ¯ X Q$ also has the length of $¯ ¯¯¯¯¯¯ ¯ A B$ .)