Question

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

Answer 1

Hint:Draw a line segment of length 7.5 cm with the help of scale and pencil and name the point as according to the question. Measure another length of line segment from one of the points of the previous line. Use scale to get a perfect straight line.

Complete step-by-step answer:
Given lengths of line segments AB and CD in the question are
AB = 7.5 cm
CD = 2.5 cm
As, here we need to draw a line segment of length AB + CD. So, we can draw a line segment of AB or CD and then draw another line from the extreme of one end of the first line.
So, construction with steps are given as
(i) using a scale and pencil measure a distance of 7.5 cm and draw a length 7.5 cm. Name the ends of these line segments as A and B.

(ii) Now, measure another length of line segment starting from point B of 2.5 cm. It means put your scale at point B and extend it to 2.5 cm by taking care that the line segment AB and another line extended from point B are in a straight line

(iii) Name the end points of another line segment as C and D. B and C are the same points.
(iv) Hence, line segment AD of 7.5 + 2.5 = 10 cm is drawn in the diagram

Note: Another approach for the question would be that we can make a line segment of 10 cm directly as well. And hence, divide it in two parts of lengths 7.5 cm and 2.5 cm. So, one may follow this approach as well.Don’t make the line CD in another direction in the solution. It should lie in the same direction of AB.