Question

If AB = 7.5 cm and CD = 2.5 cm, construct a segment whose length is equal to

(i) AB − CD
(ii) 2AB
(iii) 3CD
(iv) AB + CD
(v) 2AB + 3CD

Answer 1

Given:
AB = 7.5 cm and CD = 2.5 cm
Draw AB and CD


(i) Draw a line l and take a point E on it.
Now, take a divider and open it such that the ends of both the arms are at A and B. Then, we lift the divider and place its one end at E and other end (F) on the line l as shown in the figure. Now, reset the divider in such a way that the end of its one hand is at C and the end of other hand is at D.
Then, we lift the divider and place its one end at E and other end (G) on the line l as shown in the figure. FG is required line segment, whose length is equal to (AB − CD).

(ii) Draw a line l and take a point E on it. Now take a divider and open it such that the ends of both its arms are at A and B.
Then, we lift the divider and place its one end at E and other end (say F) on the line l as shown in the figure.
Again, lift the divider and place its one end at F and other end on the line l, opposite to E.
Let this point be G.
EG is required line segment, whose length is equal to 2AB.

(iii) We draw a line l and take a point E on it. Now, take a divider and open it such that the ends of both its arms are at C and D.
Then, we lift the divider and place its one end at E and other end (F) on the l, as shown in the figure.
Again, lift the divider end (G) on the line l opposite to C.
Again, lift the divider and place its one end at G and another end (H) on the line l, opposite to E.
EH is required line segment, whose length is equal to 3CD.





(iv) We draw a line l and take a point E on it. Now, take a divider and open it such that the ends of both its arms are at A and B. Then, we lift the divider end (F) on the line l, as shown in the figure.
Now, reset the divider in such a way that the end of its one hand is at C and the end of other hand is at D.
Then, we lift the divider and place its one end at F and another end (G) on the line l opposite to E, as shown in the figure.
EG is required line segment, whose length is equal to (AB + CD).

(v) Draw a line l and take point E on it. Now, take a divider and open it such that the ends of both its arms are at A and B. Then, we lift the divider and place its one end at E and other end (say F) on the line l, as shown in the figure.
Again, lift the divider and place its one end at F and another end (G) on the line l, opposite to E.
Now, reset the divider in such a way that the ends of its one hand is at C and the end of other hand is at D.
Then, we lift the divider and place its one end at G and another end (say H) on the line l, opposite to E as shown in the figure.
Again, lift the divider and place its one end at H and other end (say I) on the line l, opposite to E as shown in the figure.
Again, lift the divider and place its one end at I and another end (say J) on the line l, opposite to E as shown in the figure.
EG is required line segment, whose length is equal to (2AB + 3CD).