Question

Find the diagonal of a quadrilateral whose area is 756cm² and the perpendicular from the opposite vertices are 17cm and 19cm.

Answer 1

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.