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Question

Question 4

Given ¯¯¯¯¯¯¯¯AB of length 3.9 cm, construct ¯¯¯¯¯¯¯¯PQ such that the length ¯¯¯¯¯¯¯¯PQ is twice that of AB . Verify by measurement.

(Hint: Construct ¯¯¯¯¯¯¯¯¯PX such that length of ¯¯¯¯¯¯¯¯¯PX = length of ¯¯¯¯¯¯¯¯AB;
then cut off ¯¯¯¯¯¯¯¯¯XQ such that ¯¯¯¯¯¯¯¯¯XQ also has the length of ¯¯¯¯¯¯¯¯AB.)

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Solution

Steps of construction:

(i) Draw a line 'l'.
(ii) Construct ¯¯¯¯¯¯¯¯¯PX such that length of ¯¯¯¯¯¯¯¯¯PX = length of ¯¯¯¯¯¯¯¯AB
(iii) Then cut of ¯¯¯¯¯¯¯¯¯XQ such that ¯¯¯¯¯¯¯¯¯XQ also has the length of ¯¯¯¯¯¯¯¯AB.
(iv) Thus the length of ¯¯¯¯¯¯¯¯¯PX and the length of ¯¯¯¯¯¯¯¯¯XQ added together make twice the length of ¯¯¯¯¯¯¯¯AB

Verification:

By measurement, we find that PQ = 7.8

= 3.9 cm + 3.9 cm

= ¯¯¯¯¯¯¯¯AB + ¯¯¯¯¯¯¯¯AB = 2 x ¯¯¯¯¯¯¯¯AB


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