{"id":27559,"date":"2021-07-01T10:38:19","date_gmt":"2021-07-01T05:08:19","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=27559"},"modified":"2021-07-01T10:38:19","modified_gmt":"2021-07-01T05:08:19","slug":"ncert-solutions-for-class-7-maths-chapter-6-ex-6-4","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-7-maths-chapter-6-ex-6-4\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4"},"content":{"rendered":"

These NCERT Solutions for Class 7 Maths<\/a> Chapter 6 The Triangles and Its Properties Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Exercise 6.4<\/h2>\n

Question 1.
\nIs it possible to have a triangle with the following sides?
\n(i) 2 cm, 3 cm, 5 cm
\n(ii) 3 cm, 6 cm, 7 cm
\n(iii) 6 cm, 3 cm, 2 cm
\nAnswer:
\n(i) 2 cm, 3 cm, 5 cm
\n2 cm + 3 cm = 5 cm
\nthird side = 5 cm
\n\u2235 Sum of the measures of length of two sides = length of the third side
\n\u2234 It is not possible with these sides to form a triangle.<\/p>\n

(ii) 3 cm, 6 cm, 7 cm
\n3 cm + 6 cm = 9 cm
\n9 cm > 7 cm
\n3 cm + 7 cm = 10 cm and 10 cm > 6 cm.
\n6 cm + 7 cm = 13 cm and 13 cm > 3 cm.
\nThus, a triangle can be possible with these sides.<\/p>\n

(iii) 6 cm, 3 cm and 2 cm.
\n6 cm + 3 cm = 9 cm and 9 cm > 2 cm
\n3 cm + 2 cm = 5 cm and 5 cm < 6 cm 2 cm + 6 cm = 8 cm and 8 cm > 5 cm
\nThus, a triangle cannot be possible with these sides.<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nTake any point O in the interior of a triangle PQR. Is
\n(i) OP + OQ > PQ?
\n(ii) OQ + OR > QR?
\n(iii) OR + OP > RP?
\n\"NCERT
\nAnswer:
\n(i) Yes OP + QQ> PQ
\n( The sum of lengths of any two sides of a triangle is greater than the length of the third side)
\n(ii) Yes, OQ + OR > QR
\n(iii) Yes, OR + OP > RP<\/p>\n

Question 3.
\nAM is a median of a triangle ABC. IsAB + BC + CA > 2 AM?
\n(Consider the sides of triangles \u0394ABM and \u0394AMC.)
\nAnswer:
\nSince, the sum of the length of any two sides of a triangle is greater than the length
\nof the third side
\n\u2234 In \u0394ABM, we have
\n(AB + BM) > AM …………. (i)
\nSimilarly in \u0394ACM
\n(CA + CM) > AM ………. (ii)
\n\"NCERT
\nAdding (1) and (2), we have
\n[ (AB + BM) + (CA + CM)] > AM + AM
\n[ AB + (BM + CM) + CA] > 2 AM
\n[ AB + BC + CA]> 2AM
\nThus, (AB + BC + CA) > 2 AM<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nABCD is a quadrilateral.
\nIs AB + BC + CD + DA > AC + BD?
\nAnswer:
\nThe sum of the lengths of any two sides of a triangle is greater than the length of the third side.
\n\"NCERT
\nIn ABC, we have
\nAB + BC > AC …………(i)
\nSimilarly, in \u0394ACD, we have
\nCD + DA > AC …………(ii)
\nAdding (i) and (ii), we get
\n[(AB + BC) + (CD + DA)] > 2 AC …………(iii)
\nAgain In \u0394ABD, we have
\nAB + DA > BD …………….(iv)
\nIn \u0394BCD, we have
\nBC + CD > BD …(v)
\nAdding (iv) and (v), we get
\n[(AB + DA) + (BC + CD)] > 2 BD …………..(vi)
\nNow Adding (iii) and (vi), we get
\n2[(AB + BC) + (CD+ DA)] > 2 (AC + BD) (AB + BC + CD + DA) > (AC + BD)<\/p>\n

Question 5.
\nABCD is a quadrilateral.
\nIs AB + BC + CD + DA < 2(AC + BD)?
\nAnswer:
\nSince the sum of the length of any two sides of a triangle is greater than the length of the third side.
\n\"NCERT
\n\u2234 In \u0394AOB, we have (OA + OB) > AB …………(i)
\nSimilarly,
\nIn \u0394OBC, we have
\n(OB + OC) > BC …………..(ii)
\nIn \u0394OCD, we have
\n(OC + OD) > CD ………….(iii)
\nIn \u0394OAD we have
\n(OA + OD) > AD …………..(iv)
\nAdding (i), (ii), (iii) and (iv), we have
\n2] OA + OB + OC + OD] > (AB + BC + CD + DA)]
\n\u21d2 AB + BC + CD + DA < 2 (OA + OB + OC + OD)
\n\u21d2 AB + BC + CD + DA < 2 [(OA + OC) + (OB + OD)]
\n\u21d2 AB + BC + CD + DA < 2 (AC + BD)<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nThe lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
\nAnswer:
\nSince, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
\nSum of 12 cm and 15 cm is greater than the length of the third side,
\ni.e. (12 cm + 15 cm) > Third side 27 cm > Third side (or) Third side < 27 cm.
\nAlso, the difference of the lengths of any two sides is less than the length of the third side.
\n(15 cm – 12 cm) < Third side 3 cm < Third side
\nThus, we have 3 cm < Third side < 27 cm.
\n\u2234 The third side should be of any length between 3 cm and 27 cm.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Exercise 6.4 Question 1. Is it possible to have a triangle with the following sides? …<\/p>\n

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[9],"tags":[],"yoast_head":"\nNCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-7-maths-chapter-6-ex-6-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 Questions and Answers are prepared by our highly skilled subject experts. 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