Q. 1

# ∠B is a right angle in ΔABC and is an altitude to hypotenuse. AB = 8, BC = 6. Find the area of ΔBDC.

Answer :

In ∆ABC, ∠B is a right angle, AB = 8 and BC = 6

= 24 …(1)

In ∆ABC, ∠B is a right angle and BD is an altitude,

In ∆ABC,

∠A + ∠C = 90⁰ and,

In ∆BDC,

∠DBC + ∠C = 90⁰

So, ∠A = ∠DBC …(2)

In ∆ABC and ∆BDC,

∠DAB ≅ ∠DBC [from (2)]

∠ADB ≅ ∠BDC [by right angles]

The correspondence ADB ↔ BDC is a similarity by AA corollary.

Areas of similar triangles are proportional to the squares of their corresponding sides.

…(3)

Now, ADB + BDC = ABC

BDC = 8.64

The area of ∆BDC is 8.64.

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