Mathematics
In the given figure, ∠ABC = 90° and BD ⟂ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Related Questions
In the given figure, DE ∥ BC and BD = DC.
(i) Prove that DE bisects ∠ADC.
(ii) If AD = 4.5 cm, AE = 3.9 cm and DC = 7.5 cm, find CE.
(iii) Find the ratio AD : DB.

In the given figure, BA ∥ DC. Show that ΔOAB ∼ ΔODC. If AB = 4 cm, CD = 3 cm, OC = 5.7 cm and OD = 3.6 cm, find OA and OB.

Given that ΔABC ∼ ΔPQR.
(i) If ar(ΔABC) = 49 cm2 and ar(ΔPQR) = 25 cm2 and AB = 5.6 cm, find the length of PQ.
(ii) If ar(ΔABC) = 28 cm2 and ar(ΔPQR) = 63 cm2 and PR = 8.4 cm, find the length of AC.
(iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm2 determine ar(ΔPQR).