Triangle ABC v2

The area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.

Correct answer:

x =  -8 cm

Step-by-step explanation:

S=12 sin 30° = h/x  h = x sin30° S = 1/2 (x+2)h S = 1/2 (x+2)x. sin30° 12 = 1/2 ⋅  0.5 x(x+2) 12=1/2⋅ 0.5x⋅ (x+2)  12=1/2⋅ 0.5 x⋅ (x+2) −0.25x2−0.5x+12=0 0.25x2+0.5x−12=0  a=0.25;b=0.5;c=−12 D=b2−4ac=0.52−4⋅0.25⋅(−12)=12.25 D>0  x1,2​=2a−b±D​​=0.5−0.5±12.25​​=−1±49​ x1,2​=−1±7 x1​=6 x2​=−8 x>0 , x>2 x=x2​=(−8)=−8 cm

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