Given ABC is a triangle with altitudes of length 2, 4 & λ units, then
(i) Least integer value of λ is
Text Solution
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Ans.
(i)
Sol. 2 = 
⇒ a = Δ
4 = 
⇒ b = 
λ = 
⇒ c = 
∴ | a – b | < c < ( a + b)
< 
< 
< 
< 
< λ < 4
⇒ λ = 2 , 3 (integer values of λ )
if λ = 3 then a = Δ , b = 
, c = 
using cosine rule, we get cos A < 0
∴ Δ ABC is obtuse angled
(ii)
Sol. 2 = 
⇒ a = Δ
4 = 
⇒ b = 
λ = 
⇒ c = 
∴ | a – b | < c < ( a + b)
< 
< 
< 
< 
< λ < 4
⇒ λ = 2 , 3 (integer values of λ )
if λ = 3 then a = Δ , b = 
, c = 
using cosine rule, we get cos A < 0
∴ Δ ABC is obtuse angled
(iii)
Sol. 2 = 
⇒ a = Δ
4 = 
⇒ b = 
λ = 
⇒ c = 
∴ | a – b | < c < ( a + b)
< 
< 
< 
< 
< λ < 4
⇒ λ = 2 , 3 (integer values of λ )
if λ = 3 then a = Δ , b = 
, c = 
using cosine rule, we get cos A < 0
∴ Δ ABC is obtuse angled
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