RD Sharma Solutions for Class 10 Chapter 11 Constructions Exercise 11.1

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	Exercise 11.1 Exercise 11.2 Exercise 11.3
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 :

1. Draw a line segment AB = 12 cm.
2. Draw a ray AX at A making an acute angle with AB.
3. From B, draw another ray BY parallel to AX.
4. Cut off 2 equal parts from AX and 3 equal parts from BY.
5. Join 2 and 3 which intersects AB at P.

P is the required point which divides AB in the ratio of 2 : 3 internally.

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 :

1. Draw a line segment AB = 9 cm.
2. Draw a ray AX making an acute angle with AB.
3. From B, draw another ray BY parallel to AX.
4. Cut off 4 equal parts from AX and 3 parts from BY.
5. Join 4 and 3 which intersects AB at P.

P is the required point which divides AB in the ratio of 4 : 3 internally.

3. Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also justify your construction.

Solution

Steps of construction :

1. Draw a line segment AB = 14 cm.
2. Draw a ray AX making an acute angle with AB.
3. From B, draw another ray BY parallel to AX.
4. From AX, cut off 2 equal parts and from B, cut off 5 equal parts.
5. Join 2 and 5 which intersects AB at P.

P is the required point which divides AB in the ratio of 2 : 5 internally.

4. Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5.

Solution

Steps of construction :

1. Draw a line segment AB = 8 cm.
2. Draw a ray AX making an acute angle with ∠BAX = 60° with AB.
3. Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.
4. Mark four points A₁, A₂, A₃, A₄ on AX and five points B₁, B₂, B₃, B₄, B_s on BY in such a way that AA₁ = A₁A₂ = A₂A₃ = A₃A₄ .
5. Join A₄B₅.
6. Let this line intersect AB at a point P.

Thus, P is the point dividing the line segment AB internally in the ratio of 4 : 5.