NCERT Solutions for Class 7 Maths<\/a> Chapter 6 The Triangles and Its Properties Ex 6.5 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 6.5<\/h2>\n Question 1. \nPQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR. Ans: In the right APQR \nAnswer: \nIn the right \u0394PQR \n \nQR2<\/sup> = PQ2<\/sup> + PR2<\/sup> \n(pythagoras property) \n= 102<\/sup> + 242<\/sup> \n= 100 + 576 \n= 676 \nQR2<\/sup> = 262<\/sup> \n\u2234 QR = 26 cm<\/p>\n <\/p>\n
Question 2. \nABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC. \nAnswer: \nIn the right \u0394ABC \n \nAB2<\/sup> = AC2<\/sup> + BC2<\/sup> \n(using pythagoras property) \n252<\/sup> = 72<\/sup> + BC2<\/sup> \n625 = 49 + BC2<\/sup> \n625 – 49 = BC2<\/sup> \n576 = BC2<\/sup> \n242<\/sup> = BC2<\/sup> \n\u2234 BC = 24 cm<\/p>\nQuestion 3. \nA 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall. \nAnswer: \nLet the distance of the foot of a ladder from the wall be \u2018a\u2019m \n \na22<\/sup> + 122<\/sup> = 152<\/sup> \n(using pythagoras property) \na2<\/sup> + 144 = 225 \na2<\/sup> = 225 – 144 \na2<\/sup> = 81 \na2<\/sup> = 92<\/sup> \na = 9 m \nThe distance of the foot of the ladder from the wall = 9 m.<\/p>\n <\/p>\n
Question 4. \nWhich of the following can be the sides of a right triangle? \n(i) 2.5 cm, 6.5 cm, 6 cm. \n(ii) 2 cm, 2 cm, 5 cm. \n(iii) 1.5 cm, 2 cm, 2.5 cm. \nIn the case of right-angled triangles, identify the right angles. \nAnswer: \n(i) 2.5 cm, 6.5 cm, 6 cm2<\/sup>. \nThe longest side is 6.5 cm \n2.52<\/sup> + 62<\/sup> = 6.25 + 36 \n= 42.25 \n6.52<\/sup> = 42.25 \n\u2234 6.52<\/sup> = 2.52<\/sup> + 62<\/sup> \n(pythagoras property) \nThe given lengths can be the sides of a right triangle. \nThe right angle is the angle between the sides 2.5 cm and 6 cm<\/p>\n(ii) 2 cm, 2 cm, 5 cm \nThe longest side is 5 cm \n22<\/sup> + 22<\/sup> = 4 + 4 = 8 \n52<\/sup> = 25 \n52<\/sup> \u2260 22<\/sup> + 22<\/sup> \n\u2234 The given length cannot be the sides of a right triangle.<\/p>\n(iii) 1.5 cm, 2 cm, 2.5 cm \nThe longest side is 2.5 cm \n1.52<\/sup> + 22<\/sup> = 2.25 + 4 \n= 6.25 \n2.52<\/sup> = 6.25 \n1.52<\/sup> + 22<\/sup> = 2.52<\/sup> \n(pythagoras property) \nThe given lengths can be sides of a right triangle. \nThe right angle is the angle between the sides 1.5 cm and 2 cm.<\/p>\nQuestion 5. \nA tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree. \n \nAnswer: \nLet the tree BD be broken at the point C, such that CD = CA \nIn the right triangle ABC, using the pythagoras property; we get \nAC2<\/sup> = AB2<\/sup> + BC2<\/sup> \nAC2<\/sup> = 122<\/sup> + 52<\/sup> \n= 144 + 25 \nAC2<\/sup> = 169 \nAC2<\/sup> = 132<\/sup> \n\u2234 AC = 13 \nNow, height of the tree \nBD = BC + CD (CD = AC) \n= 5 m + 13 m \n= 18 m \nThe height of the tree is 18 m.<\/p>\n <\/p>\n
Question 6. \nAngles Q and R of PQR are 25\u00b0 and 65\u00b0. Write which of the following is true: \n(i) PQ2<\/sup> + QR2<\/sup> = RP2<\/sup> \n(ii) PQ2<\/sup> + RP2<\/sup> = QR2<\/sup> \n(iii) RP2<\/sup> + QR2<\/sup> = PQ2<\/sup> \nAnswer: \nIn \u0394PQR \n\u2220P + \u2220Q +\u2220R = 180\u00b0 \n\u2220P + 25\u00b0 + 65\u00b0 = 180\u00b0 \n \n\u2220P + 90\u00b0 = 180\u00b0 \n\u2220P = 180\u00b0 – 90\u00b0 \n= 90\u00b0 \nSo, \u0394PQR is a triangle right angled at P. \n\u2234 QR is the hypotenuse. \n\u2234 using the pythagoras property \nQR2<\/sup> = PQ2<\/sup> + PR2<\/sup> So,<\/p>\n(ii) PQ2<\/sup> + RP2<\/sup> = QR2<\/sup> is true<\/p>\nQuestion 7. \nFind the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm. \nAnswer: \nLet the breadth AD be x cm. \nIn the right triangle ABD, \n \nBD2<\/sup> = AD2<\/sup> + AB2<\/sup> \n412<\/sup>= x2<\/sup> + 402<\/sup> \nx2<\/sup> = 412<\/sup> – 402<\/sup> \n= 1681 – 1600 \nx2<\/sup> = 81 \nx2<\/sup> = 92<\/sup> \nx = 9 cm \nPerimeter of the rectangle = 2 (l + b) \n= 2 (40 + 9) \n= 2 \u00d7 49 \n= 98 cm \nThus, the perimeter of the rectangle \n= 98 cm<\/p>\n <\/p>\n
Question 8. \nThe diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter. \nAnswer: \nSince the diagonals of a rhombus bisect each other at right angles. \n \n\u2220AOB = \u2220BOC = \u2220COD = \u2220AOD = 90\u00b0 \nAO = \\(\\frac { 1 }{ 2 }\\) AC; AO = \\(\\frac { 1 }{ 2 }\\) \u00d7 30 = 15 \n\u2235 AO = OC = 15 cm and BO = OD = 8 cm \nIn the right \u0394AOB, \nAB2<\/sup> = AO2<\/sup> + BO2<\/sup> \nAB2<\/sup> = 152<\/sup> + 82<\/sup> \nAB2<\/sup> = 225 + 64 \nAB2<\/sup> = 289 \nAB2<\/sup> = 172<\/sup> \nAB = 17 cm \n\u2235 Side of the rhombus is 17 cm. \n\u2234 Perimeter of the rhombus ABCD = 4 \u00d7 17 \n(all the four sides are equal) = 68 cm<\/p>\n","protected":false},"excerpt":{"rendered":"These NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.5 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 6.5 Question 1. PQR is a triangle, right-angled at P. If PQ = 10 …<\/p>\n
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.5<\/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 6.5 - 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