Question

ABC is a right triangle with AB=AC. If bisector of angle A meets BC at D and AD=2√2cm,then the perimeter of ∆ABC

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Answer 1

angle was not connected

Answer 2

In ∆ABD and ∆ACD

AB = AC (given)

∠BAD = ∠CAD

As AD is bisector of ∠A and AD = AD ⇒ ∆DAB =

∆DAC

(by SAS congruency rule) ⇒ ∠ADB = ∠ADC (by c.p.c.t)

⇒ ∠ADB = ∠ADC = 90° and BD = DC In ∆ABD, AD2 + BD2 = AB2 …(i)

⇒ AD2 + DC2 = AC2

…(ii) Adding (i) and (ii),

we get 2 AD2 + BD2 + DC2 = AB2 + AC2

⇒ 2AD2 + BD2 + DC2 = BC2

⇒ 2 AD2 + 2BD2 = BC2

⇒ 2 (AD2 + BD2) = BC2

⇒ 4 AD2 = BC2

⇒ 2 AD = BC

i.e. BC = 2AD