RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1 (Updated for ) • cbseBoy

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.
RD Sharma Class 10 Chapter 11 Constructions

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.
Constructions Class 10 RD Sharma

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.
RD Sharma Class 10 Solutions Constructions

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.
RD Sharma Class 10 Solutions Constructions Exercise 11.1
(iii) Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.
(iv) 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 .
(v) Join A₄B₅.
(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.