The lengths of the diagonals of a rhombus are 24 cm and 32 cm, then the length of the altitude of the rhombus is

(a) 12cm   (b) 12.8cm   (c) 19 cm  (d) 19.2cm

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 4 The lengths of the diagonals of a rhombus are 24 cm and 32 cm, then the length of the altitude of the rhombus is (a) 12cm (b) 12.8cm (c) 19 cm (d) 19.2cm Let ABCD be the given rhombus Where AC = 32 cm and BD = 24 cm First, let’s find the sides of rhombus We know that, Diagonals of rhombus are perpendicular bisector of each other ∴ AC ⊥ BD And OB = 𝐵𝐷/2 = 24/2 = 12 cm OA = 𝐴𝐶/2 = 32/2 = 16 cm Now, In Right triangle ∆AOB By Pythagoras Theorem, 〖𝐴𝐵〗^2 = 〖(𝑂𝐴)〗^2 + 〖(𝑂𝐵)〗^2 〖𝐴𝐵〗^2 = 〖(16)〗^2 + 〖(12)〗^2 〖𝐴𝐵〗^2 = 256 + 144 〖𝐴𝐵〗^2 = 400 〖𝐴𝐵〗^2 = 〖(20)〗^2 Cancelling square AB = 20 cm Now, To find Altitude, We use the help of Area Area using Diagonals Area of Rhombus = 1/2 × Diagonal 1 × Diagonal 2 = 1/2 × 24 × 32 = 384 cm2 Area using Base and Height Area of Rhombus = Base × Height Putting Area = 384 cm2, Base = Side of Rhombus = 20 cm 12 × 32 = 20 × Height 12 × 32 × 1/20 = Height 19.2 = Height Height = 19.2 cm So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.