The angles of a triangle are in the ratio 1 1 4 If the perimeter of the triangle is k times its larg...........

Quantitative Aptitude (CDS) Mensuration 2D

The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k?

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

$1-\frac{2}{\sqrt{3}}$

$2+\frac{2}{\sqrt{3}}$

4k + k + k = 6x =180 degrees

k= 30 degrees

So triangle is 30,30 and 120 degrees

Let sides of triangle be x,x and y units with y being the largest side opposite to 120 degree angle

Using cosine law

Cos 120 = - sin 30 = -1/2 = (2x² – y²)/2x² So 3x² = y² …. (i) Given Perimeter = k (Largest side) Or 2x+y = ky Putting value of x from eq (i)

2y/√3 + y = ky

K = 2/√3 + 1

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