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Ex 6.5, 8 - The diagonals of a rhombus measure 16 cm and 30 cm

Ex 6.5, 8 - Chapter 6 Class 7 Triangle and its Properties - Part 2
Ex 6.5, 8 - Chapter 6 Class 7 Triangle and its Properties - Part 3

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Transcript

Ex 6.5, 8 The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter In a rhombus All sides are equal Diagonals are perpendicular Let ABCD be the given rhombus Where BD = 16 cm and AC = 30 cm We know that, Diagonals of rhombus are perpendicular bisector of each other ∴ AC ⊥ BD And OB = 𝐵𝐷/2 = 16/2 = 8 cm OA = 𝐴𝐶/2 = 30/2 = 15 cm Now, In ∆AOB, right angled at O, By Pythagoras Theorem, 〖𝐴𝐵〗^2 = 〖(𝑂𝐴)〗^2 + 〖(𝑂𝐵)〗^2 〖𝐴𝐵〗^2 = 〖(15)〗^2 + 〖(8)〗^2 〖𝐴𝐵〗^2 = 225 + 64 〖𝐴𝐵〗^2 = 289 〖𝐴𝐵〗^2 = 〖(17)〗^2 Cancelling square AB = 17 cm Now, Perimeter ABCD = AB + BC + CD + AD = AB + AB + AB + AB = 4 × AB = 4 × 17 = 68 cm Hence, required perimeter is 68 cm (Since sides of rhombus are equal)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.