Question

In a DABC, 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

Ž $\frac { \mathrm { a } } { \sin 45 ^ { \circ } }$ = $\frac { \mathrm { b } } { \sin 75 ^ { \circ } }$ = $\frac { c } { \sin 60 ^ { \circ } }$

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

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

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