Question

ABCD is a trapezium such that AB || CD. If AC2 + BD2 13 cm and √AC x BD = 2√15 cm, then the sum of cubes of lengths of diagonals of ABCD is

Answer 1

ABCD is a trapezium such that AB and CD are parallel and BC⊥CD. If ∠ADB=θ, BC=p and CD=q, then AB is equal to

cosα=

p

2

+q

2

q

and sinα=

p

2

+q

2

p

Using sine rule in triangle ABD

sinθ

AB

=

sin(θ+α)

BD

⇒AB=

sinθcosα+cosθsinα

p

2

+q

2

sinθ

=

p

2

+q

2

sinθ⋅q

+

p

2

+q

2

cosθ⋅p

p

2

+q

2

sinθ

⇒AB=

(pcosθ+qsinθ)

(p

2

+q

2

)sinθ

Answer 2

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