## 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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Last updated at April 16, 2024 by Teachoo

This question is

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

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)