In this chapter, we provide RD Sharma Class 10 Ex 11.1 Solutions Chapter 11 Constructions for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 10 Ex 11.1 Solutions Chapter 11 Constructions pdf, Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 11 |

Chapter Name | Constructions |

Exercise | 11.1 |

Category | RD Sharma Solutions |

Table of Contents

**RD Sharma Solutions for Class 10 Chapter** **11**** Constructions** Ex 11.1 Download PDF

**Constructions**Ex 11.1 Download PDF

**Chapter 11: Constructions Exercise – 11.1**

**Question: 1**

Determine a point which divides a line segment of length 12 cm internally in the ratio of 2: 3. Also, justify your construction.** **

**Solution:**

Steps of Construction:

1. Draw a line segment AB of 12 cm

2. Through the points A and B draw two parallel line on the opposite side of AB

3. Cut 2 equal parts on AX and 3 equal parts on BY such that AX_{1} = X_{1}X_{2} and BX_{1 }= Y_{1}Y_{2} = Y_{2}Y_{3}.

4. Join X_{2}Y_{3} which intersects AB at P

∴ AP/PB = 2/3.

Justification:

In ΔAX_{2}P and ΔBY_{3}P, we have

∠APX_{2} = ∠BPY_{3} {Because they are vertically opposite angle}

∠X_{2}AP = ∠Y_{3}BP {Because they are alternate interior angles}

ΔAX_{2}P ΔBY_{3}P {Because AA similarity}

∴ AP/BP = AX_{2}/BY_{3 }= 2/3 {Because of C.P.C.T}

**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:

1. Draw a line segment AB of 9 cm

2. Through the points, A and B, draw two parallel lines AX and BY on the opposite side of AB

3. Cut 4 equal parts on AX and 3 equal parts on BY such that: AX_{1} = X_{1}X_{2} = X_{2}X_{3 }= X_{3}X_{4} and BY_{1} = Y_{1}Y_{2} = Y_{2}Y_{3}

4. Join X_{4}Y_{3} which intersects AB at P

∴ AP/PB = 4/3

Justification:

In ΔAPX_{4} and ΔBPY_{3}, we have

∠APX_{4} = ∠BPY_{3} {Because they are vertically opposite angles}

∠PAX_{4} = ∠PBY_{3} {Because they are alternate interior angle}

ΔAPX_{4} ΔBPY_{3} {Because AA similarity}

∴ PAPB = AX_{4}/BY_{3} = 4/3 {Because of C.P.C.T}

**Question: 3**

Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, give justification for the construction.

**Solution:**

Steps of construction:

1. Draw a line segment AB of 14 cm

2. Through the points A and B, draw two parallel lines AX and BY on the opposite side of AB

3. Starting from A, Cut 2 equal parts on AX and starting from B, cut 5 equal parts on BY such that: AX_{1} = X_{1}X_{2} and BY_{1} = Y_{1}Y_{2} = Y_{2}Y_{3} = Y_{3}Y_{4} = Y_{4}Y_{5}

4. Join X_{2}Y_{5} which intersects AB at P

∴ AP/PB = 2/5

Justification:

In ΔAPX_{2} and ΔBPY_{5}, we have

∠APX_{2} = ∠BPY_{5} {Because they are vertically opposite angles}

∠PAX_{2} = ∠PBY_{5} {Because they are alternate interior angles}

Then, ΔAPX_{2} ΔBPY_{5} {Because AA similarity}

∴ AP/PB = AX_{2}/BY_{5} = 2/5 {Because of C.P.C.T}

**All Chapter RD Sharma Solutions For Class10 Maths**

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