{"id":15074,"date":"2020-09-10T14:32:37","date_gmt":"2020-09-10T09:02:37","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=15074"},"modified":"2021-07-02T15:01:53","modified_gmt":"2021-07-02T09:31:53","slug":"kseeb-solutions-for-class-7-maths-chapter-6-ex-6-4","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-7-maths-chapter-6-ex-6-4\/","title":{"rendered":"KSEEB Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4"},"content":{"rendered":"

Students can Download Chapter 6 The Triangles and Its Properties Ex 6.4, Question and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths<\/a>, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.<\/p>\n

Karnataka State Syllabus Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4<\/h2>\n

Question 1.
\nIs it possible to have a triangle with the following sides ?
\ni) 2 cm, 3 cm, 5 cm.
\nSolution:
\ngreatest side is 5 cms.
\n2 + 3 = 5
\nHere sum of the side is equal to third side.
\nSo it is impossible to construct the triangle by given measures.
\nBecause the property of a triangle says that the sum of the two sides of a triangle is greater than the length of the third side.<\/p>\n

ii) 3 cm, 5 cm, 7 cm
\nSolution:
\nThe greatest side is 7 cm.
\n3 + 6 = 9 cms > 7
\n6 + 7 = 13 > 3
\n7 + 3 = 10 > 6
\n\u2234 It is possible to construct the triangle with the sides of 3, 6 and 7 cms.<\/p>\n

\"KSEEB<\/p>\n

iii) 6 cm, 3 cm, 2 cm
\n6 + 3 = 9 > 2
\n3 + 2 = 5 > 6
\n2 + 6 = 8 > 3
\n\u2234 It is not possible to construct the triangle with the sides of 6, 3 and 2 cms.<\/p>\n

Question 2.
\nTake any point \u2018O\u2019 in the interior of a triangle PQR. Is
\n\"KSEEB
\ni) OP + OQ > PQ
\nSolution:
\nYes. Sum of the length of any two sides of a triangle is greater than the length of the 3 side.<\/p>\n

ii) OQ + OR > QR
\nSolution:
\nYes, Sum of the length of any two sides of a triangle is greater than the length of the 3rd<\/sup> side.<\/p>\n

iii) OR + OP > RP
\nSolution:
\nYes, Sum of the length of any two sides of a triangle is greater than the length of the 3rd<\/sup> side.<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nAM is a median of a triangle ABC. Is AB + BC + CA > 2 AM ?
\n(Consider the sides of triangles \u2206 ABM and \u2206 AMC.)
\nSolution:
\n\"KSEEB
\nConsider the triangle ABM
\nIn \u2206 ABM
\nAB + BM > AM \u2014 1 (Sum of the length of any 2 sides of a triangle is greater that the 3rd<\/sup> side.)
\nIn \u2206 ACM
\nCM + CA > AM \u2014 2 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nAdd 1 and 2
\n(AB + BM) + (CM + CA) > AM + AM
\nAB + (BM + CM) + CA > 2AM
\nAB + BC + CA > 2AM (yes, it is proved.)<\/p>\n

Question 4.
\nABCD is a quadrilateral.
\nIs AB + BC + CD + DA > AC + BD?
\nSolution:
\n\"KSEEB
\nConsider the \u2206 ABC
\nAB + BC > CA \u2014 1 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nIn \u2206 ACD
\nAD + CD > AC \u2014 2 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nAdding 1 and 2
\nAB + BC + CD + DA > 2AC \u2014 3
\nIn \u2206 ABD
\nAB + DA > BD \u2014 4 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nIn \u2206 BCD
\nBC + CD > BD \u2014 5 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nAdding 4 and 5
\nAB + DA + BC + CD > 2BD \u2014 6
\nAdding 3 and 6
\n\"KSEEB
\n\u2234 AB + BC + CD + DA > AC + BD (yes, it is proved)<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD) ?
\nSolution:
\n\"KSEEB
\nIn \u2206 AOB OA + OB > AB \u2014 1 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nIn \u2206 BOC
\nOB + OC > BC \u2014 2 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nIn \u2206 COD
\nOC + CD > CD \u2014 3 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nIn \u2206 AOD
\nOA + OD > AD \u2014 4 (Sum of the length of any 2 sides of a triangle is greater than the 3rd<\/sup> side.)
\nAdd all the 4
\n\"KSEEB
\n\u2234 AB + BC + CD + DA< 2 (AC + BD) (proved)<\/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?
\nSolution:
\nLet \u2018x\u2019 cm to the length of the 3rd<\/sup> side.
\nAccording to the sum of the length of any 2 sides of a triangle is greater than 3rd<\/sup>\u00a0side.
\n\u2234 12 + 15 >x
\n27 > x
\nor x < 27 15 + x > 12
\nx > 12 \u2013 15 = -3
\nx + 12 > 15
\nx > 15 \u2013 12 = 3
\n\u2234 x > -3 and x > 3 we should take x > 3
\n\u2234 The length of 3rd<\/sup>\u00a0side of a triangle should be in between 3 cm and 27 cms.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Chapter 6 The Triangles and Its Properties Ex 6.4, Question and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[84],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/15074"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=15074"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/15074\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=15074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=15074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=15074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}