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
CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]
Last updated at April 16, 2024 by Teachoo
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, letβs find the sides of rhombus We know that, Diagonals of rhombus are perpendicular bisector of each other β΄ AC β₯ BD And OB = π΅π·/2 = 24/2 = 12 cm OA = π΄πΆ/2 = 32/2 = 16 cm Now, In Right triangle βAOB By Pythagoras Theorem, γπ΄π΅γ^2 = γ(ππ΄)γ^2 + γ(ππ΅)γ^2 γπ΄π΅γ^2 = γ(16)γ^2 + γ(12)γ^2 γπ΄π΅γ^2 = 256 + 144 γπ΄π΅γ^2 = 400 γπ΄π΅γ^2 = γ(20)γ^2 Cancelling square AB = 20 cm Now, To find Altitude, We use the help of Area Area using Diagonals Area of Rhombus = 1/2 Γ Diagonal 1 Γ Diagonal 2 = 1/2 Γ 24 Γ 32 = 384 cm2 Area using Base and Height Area of Rhombus = Base Γ Height Putting Area = 384 cm2, Base = Side of Rhombus = 20 cm 12 Γ 32 = 20 Γ Height 12 Γ 32 Γ 1/20 = Height 19.2 = Height Height = 19.2 cm So, the correct answer is (d)