Question 3 - Figure it out - Page 52, 53, 54 - Chapter 2 Class 8 - The Baudhayana-Pythagoras Theorem (Ganita Part 2)

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Question 3 Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units.A rhombus is a quadrilateral with all sides equal And, its diaognals bisect each other at right angles Drawing figure Let Side of rhombus = a Since diagonals bisect at O OA = OC = 𝟐𝟒/𝟐 = 12 OB = OD = 𝟕𝟎/𝟐 = 35 Also, diagonals bisect at right angles ∴ ∠ AOB = ∠ BOC = ∠ COD = ∠ AOD = 90° Now, in right triangle ∆ AOB Hypotenuse = AB = a Base = OA = 12 Height = OB = 35 By Pythagoras theorem Hypotenuse2 = Base2 + Height2 AB2 = OA2 + OB2 a2 = 122 + 352 a2 = 144 + 1225 a2 = 1369 a = √𝟏𝟑𝟔𝟗 a = √(37^2 ) a = 37 Thus, sidelength of rhombus is 37 units