RD Sharma Class 10 Solutions Chapter 11 Constructions Exercise 11.1 (Updated for 2021-22)

RD Sharma Class 10 Solutions Chapter 11 Exercise 11.1: This exercise is about figuring out how to divide a line segment and how to construct it. Students can use the RD Sharma Class 10 Solutions to have a better understanding of how to give their answers in their exams. Students can also use the RD Sharma Solutions for Class 10 Maths Chapter 11 Exercise 11.1 PDF to help them with their homework.

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RD Sharma Class 10 Solutions Chapter 11 Exercise 11.1

Access answers to RD Sharma Solutions Class 10 Maths Chapter 11 Exercise 11.1- Important Question with Answers

Question 1.
Determine a point that 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 that 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 for 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 that divides AB in the ratio of 4 : 3 internally.

Question 3.
Divide a line segment of length 14 cm internally in the ratio of 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 that 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 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.

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