Question

In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to ______

Options

• 2b

• 2c

• 3b

• 3a

Answer 1

In a ΔABC, A : B : C = 3 : 5 : 4. Then `a + b + csqrt2` is equal to 3b.

Explanation:

Let x be the common multiple.

∴ A + B + C = 12x = 180° ⇒ x = 15°

∴ A = 45°, B = 75°, C = 60°

`a/(sin45^circ) = b/(sin75^circ) = c/(sin60^circ)` = k

∴ a = `1/sqrt2`k, b = `(sqrt3 + 1)/(2sqrt2)`k, c = `sqrt3/2`k

∴ `a + b + csqrt2 = (3 + 3sqrt3)/(2sqrt2)` = 3b