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CBSE Class 10 Answered

Determine the length of altitude AD of isosceles triangle ABC of side 2a, 2a and a

Asked by dilpreet101kk | 22 Jan, 2020, 04:21: PM
Expert Answer
 
In ΔADB and ΔADC,
 
AB = AC   .... (Both are of equal length i.e. 2a)
AD = AD  .... (Common side)
angle ADB = angle ADC     ... (right angles because AD is the altitude)
→ ΔADB begin mathsize 16px style approximately equal to end styleΔADC        .... (By R.H.S congruency)
Hence, BD = CD   ... (Corresponding sides of congruent triangles)
 
BD = CD = 1/2(BC) = 1/2(a)
 
In ΔABD,
 
AB2 = AD2 + BD2
→ AD = (2a)2 - [(1/2)a]2 = 15a2 /4 
→ AD = begin mathsize 16px style fraction numerator square root of 15 straight a over denominator 2 end fraction end style

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