Question

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

• A. 2b
• B. 2c
• C. 3b
• D. 3a

Answer 1

Answer: (C)

3b

Answer 2

$A : B : C = 3 : 5 : 4$ ⇒ $A + B + C = 12 x = 180 ^ { \circ }$ ⇒ $x = 15 ^ { \circ }$

$\therefore$ $A = 45 ^ { \circ }$, $B = 75 ^ { \circ }$, $C = 60 ^ { \circ }$

i.e., $a = \frac { 1 } { \sqrt { 2 } } K , \quad b = \frac { \sqrt { 3 } + 1 } { 2 \sqrt { 2 } } K , \quad c = \frac { \sqrt { 3 } } { 2 } K$.

Hence $[ a + b + c \sqrt { 2 } ] = 3 b$.