RD Sharma Solutions Chapter 11 Constructions Exercise 11.1 Class 10 Maths
Chapter Name  RD Sharma Chapter 11 Constructions 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 11.1 Solutions
1. Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3. Also justify your construction.
Solution
Steps of construction :
 Draw a line segment AB = 12 cm.
 Draw a ray AX at A making an acute angle with AB.
 From B, draw another ray BY parallel to AX.
 Cut off 2 equal parts from AX and 3 equal parts from BY.
 Join 2 and 3 which intersects AB at P.
2. Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
Solution
Steps of construction :
 Draw a line segment AB = 9 cm.
 Draw a ray AX making an acute angle with AB.
 From B, draw another ray BY parallel to AX.
 Cut off 4 equal parts from AX and 3 parts from BY.
 Join 4 and 3 which intersects AB at P.
3. Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also justify your construction.
Solution
Steps of construction :
 Draw a line segment AB = 14 cm.
 Draw a ray AX making an acute angle with AB.
 From B, draw another ray BY parallel to AX.
 From AX, cut off 2 equal parts and from B, cut off 5 equal parts.
 Join 2 and 5 which intersects AB at P.
4. Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.
Solution
Steps of construction :
 Draw a line segment AB = 8 cm.
 Draw a ray AX making an acute angle with ∠BAX = 60° with AB.
 Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.
 Mark four points A_{1}, A_{2}, A_{3}, A_{4} on AX and five points B_{1}, B_{2}, B_{3}, B_{4}, B_{s} on BY in such a way that AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} .
 Join A_{4}B_{5}.
 Let this line intersect AB at a point P.