Answer :

To find DB

Let ∠EAD = x ----(1)

⇒ ∠ADE = 90 – x (∵ AED = 90 and sum of angles of triangle is 180)

⇒ ∠EDC = x (∵ ∠ADC = 90) ----(2)

⇒ ∠EAD = ∠EDC (by (1) and (2)) ----(3)

Now,

In ΔAED and ΔDEC

∠AED = ∠DEC (both perpendicular to AC)

∠EAD = ∠EDC (by (3))

∴ ΔAED ∼ ΔDEC

(∵ ΔAED ∼ ΔDEC)

⇒ 16×81 = ED^{2}

⇒ ED = 36 cm

⇒ 2×ED = DB = 72 cm

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