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>\nNCERT 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
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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 \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 \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
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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 \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 \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
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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":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[9],"tags":[],"yoast_head":"\nNCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.4 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n