# NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 7 |

Subject | Maths |

Chapter | Chapter 6 |

Chapter Name | The Triangle and its Properties Ex 6.4 |

Number of Questions Solved | 6 |

## NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4

**NCERT TEXTBOOK EXERCISES**

**Question 1. Is it possible to have a triangle with the following sides?**

- 2 cm, 3 cm, 5 cm
- 3 cm, 6 cm, 7 cm
- 6 cm, 3 cm, 2 cm.

**Solution:**

- Since, 2 + 3 > 5

So the given side lengths cannot form a triangle. - We have, 3 + 6 > 7, 3 + 7 > 6 and 6 + 7 > 3

i. e., the sum of any two sides is greater than the third side.

So, these side lengths form a triangle. - We have, 6 + 3 > 2, 3 + 2 > 6

So, the given side lengths cannot form a triangle.

**Question 2. Take any point O in the interior of a triangle PQR. Is**

- OP + OQ > PQ ?
- OQ + OR > QR?
- OR + OP > RP ?

**Solution:**

- Yes ! OP + OQ > PQ â€¦(1)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side - Yes! OQ + OR > QR â€¦(2)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side - Yes! OR + OP > RP â€¦(3)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

**Question 3.**

AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?

(Consider the sides of triangles âˆ† ABM and âˆ† AMC.)

**Solution:**

Using triangle inequality property in triangles ABM and AMC, we have

AB + BM > AM â€¦(1) and, AC + MC > AM â€¦(2)

Adding (1) and (2) on both sides, we get

AB + (BM + MC) + AC > AM + AM

â‡’ AB + BC + AC > 2AM

**Question 4.**

ABCD is a quadrilateral.

Is AB + BC + CD + DA > AC + BD ?

**Solution:**

In âˆ† ABC, AB + BC > AC â€¦(1)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

In âˆ† ACD, CD + DA > AC â€¦(2)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

Adding (1) and (2),

AB + BC + CD + DA > 2AC â€¦(3)

In âˆ† ABD, AB + DA > BD â€¦(4)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

In âˆ† BCD, BC + CD > BD â€¦(5)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

Adding (4) and (5),

AB + BC + CD + DA > 2BD â€¦(6)

Adding (3) and (6),

2 [AB + BC + CD + DA] > 2 (AC + BD)

â‡’ AB + BC + CD + DA > AC + BD.

**Question 5. ABCD is a quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?**

**Solution:**

In âˆ† OAB, OA + OB > AB â€¦.(1)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side.

In âˆ† OBC, OB + OC > BC â€¦.(2)

Sum of the lengths of any two sides of a triangle la greater than the length of the third side.

In âˆ† OCA,OC + OA > CA â€¦.(3)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

In âˆ† OAD, OA + OD > AD â€¦.(4)

Sum of the lengths of any two sides of a triangle is greater than the length of the third side

Adding (1), (2), (3) and (4),

2(OA + OB + OC + OD) > AB + BC + CD + DA

â‡’ AB + BC + CD + DA < 2 (OA + OB + OC + OD)

â‡’ AB + BC + CD + DA < 2(OA + OC + OB + OD)

â‡’ AB + BC + CD + DA < 2 (AC + BD).

**Question 6. The lengths of the two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?**

**Solution:**

Let x cm be the length of the third side.

âˆ´ Sum of the lengths of any two sides of a triangle is greater than the length of the third side.

âˆ´ We should have

âˆ´ The length of the third side should be any length between 3 cm and 27 cm.

## NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4 PDF

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### Class 7 Maths Chapter 6 The Triangle and its Properties

**Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1****Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.2****Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3****Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4****Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5**