## RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1

### RD Sharma Class 10 Solutions Constructions Exercise 11.1

Question 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 :

(i) Draw a line segment AB = 12 cm.

(ii) Draw a ray AX at A making an acute angle with AB.

(iii) From B, draw another ray BY parallel to AX.

(iv) Cut off 2 equal parts from AX and 3 equal parts from BY.

(v) Join 2 and 3 which intersects AB at P.

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

Question 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 :

(i) Draw a line segment AB = 9 cm.

(ii) Draw a ray AX making an acute angle with AB.

(iii) From B, draw another ray BY parallel to AX.

(iv) Cut off 4 equal parts from AX and 3 parts from BY.

(v) Join 4 and 3 which intersects AB at P.

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

Question 3.

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

Solution:

Steps of construction :

(i) Draw a line segment AB = 14 cm.

(ii) Draw a ray AX making an acute angle with AB.

(iii) From B, draw another ray BY parallel to AX.

(iv) From AX, cut off 2 equal parts and from B, cut off 5 equal parts.

(v) Join 2 and 5 which intersects AB at P.

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

Question 4.

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

Solution:

Steps of construction :

(i) Draw a line segment AB = 8 cm.

(ii) Draw a ray AX making an acute angle with ∠BAX = 60° withAB.

(iii) Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.

(iv) 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} .

(v) Join A_{4}B_{5}.

(vi) 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.

RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1

### Q1.

RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1 Q2

RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1 Q3