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The base of a triangle is 24cm and corresponding altitude is 16 cm. The area of a rhombus is equal to the area of the triangle . If one of the diagonals of the rhombus is 20 cm, find the length of the other diagonal. |
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Answer» Answer: Given, Base of the triangle,b = 24 cm Altitude,H = 16 cm Length of one diagonal, d₁ = 20 cm LET the length of the other diagonal be d₂ Area of the triangle = 1 ------ × b × h 2 1 = ------ × 24 × 16 2 = 192 cm² ∴ Area of the triangle = 192 cm² Area of rhombus = 1 ----- × d₁ × d₂ 2 Area of the triangle = Area of the rhombus 192 = 1 ----- × d₁ × d₂ 2 192 = 1 ----- × 20 × d₂ 2 192 = 10 × d₂ d₂ = 192/ 10 d₂ = 19.2 cm cm ∴ Length of the other diagonal = 19.2 |
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