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Question
Find the diagonal of a quadrilateral whose area is 756cm2 and the perpendicular from the opposite vertices are 17cm and 19cm.
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Solution
In Quadrilateral ABCD, BD is a diagonal, AM ⊥ BD, Cl ⊥ BD
AM = 17cm and CL = 19cm and Ar(Quandrilateral ABCD) = 756cm2
Let diagonal BD = x cm
Ar(Quandrilateral ABCD)
= `(1)/(2) xx "BD"("Am" + "CL")`
⇒ 756 = `(1)/(2) xx (19 + 17)`
⇒ 756 = 18x
⇒ x = 42cm.
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