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Question
Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is ______.
Options
4 cm
15 cm
16 cm
18 cm
Solution
Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is 16 cm.
Explanation:
Area of the given quadrilateral = `1/2` (Sum of altitudes) × Corresponding diagonal
⇒ `20 = 1/2(1 + 15) xx BD` ...[Given]
⇒ `1/2 xx 2.5 xx "BD = 20 cm^2`
⇒ `BD = 20 xx 2/2.5 = 40/2.5 = 16 cm`
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