Question

In a ∆ABC, A: B : C = 3 : 5 : 4.Then a + b + c $\sqrt { 2 }$ is equal to

• A. 2b
• B. 2c
• C. 3b
• D. 3a

Answer 1

Answer: (C)

3b

Answer 2

It is clear that A = 45⁰, B = 75⁰, C = 60⁰

⇒ = =

⇒ $\frac { a } { 1 / \sqrt { 2 } }$ = =

= a $\sqrt { 2 }$ = =

Now to test choice (1) we will put every thing in the expression a + b + c $\sqrt { 2 }$ in terms of b.

Indeed a + b + c $\sqrt { 2 }$

= $\frac { 2 b } { \sqrt { 3 } + 1 }$+ b + $\sqrt { 2 }$

= b$\left[ \frac { 2 } { \sqrt { 3 } + 1 } + 1 + \frac { 2 \sqrt { 3 } } { \sqrt { 3 } + 1 } \right]$= 3b

⇒ choices (1), (2) and (4) are wrong and (3) becomes true.