Construct A B - of length 7.8 c m . From this, cut off A C - of length 4. 7 c m . Measure B C - .

Steps of construction: (i) Draw a line l , Mark a point A using a sharpened pencil on l . (ii) Place the zero mark of the ruler at A . (iii) Mark a point B at a distance 7.8 c m from A . And join AB . (iv) Again, Using compasses and ruler mark a point C at a distance 4 .7 cm from A . Hence, by measuring B C - , we find that B C = 3.1 c m .

Given A B - of length 3.9 c m , construct P Q - such that the length of P Q - is twice that of A B - . 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 - .

Steps of construction: 1 . Draw a line ‘ l ’. Mark point P on the line. 2 . Measure AB using compasses as shown below. 3 . Without changing the compass cut an arc from P and mark X . 4 . From X cut an arc of the same length. By measurement, we find that P Q = 7.8 c m PQ = 3.9 c m + 3.9 c m PQ = AB - + AB - PQ = 2 × AB - Hence, line segment PQ ¯ on l with length 7 . 8 cm twice as that of A B - is constructed.