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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

(A) 9 cm  

(B) 10 cm

(C) 8 cm 

(D) 20 cm

This question is inspired from  Ex 6.5, 7 - Chapter 6 Class 10 - Triangles

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Question 4 The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is 9 cm (B) 10 cm (C) 8 cm (D) 20 cm In a Rhombus Sum of squares of sides = Sum of its diagonals (For proof, check Ex 6.5, 7 – Chapter 6 Class 10 Triangles) Thus, AB2 + BC2 + CD2 + AD2 = AC2 + BD2 Since all sides of Rhombus are equal, our equation becomes AB2 + AB2 + AB2 + AB2 = AC2 + BD2 4AB2 = AC2 + BD2 Putting length of diagonals as 16 and 12 cm 4AB2 = 162 + 122 4AB2 = 256 + 144 4AB2 = 400 AB2 = 400/4 AB2 = 100 AB2 = 102 AB = 10 cm So, the correct answer is (B) So, the correct answer is (B)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.