Sides of the triangle

Calculate triangle sides where its area is S = 84 cm² and a = x, b = x + 1, xc = x + 2

Correct result:

a = 13 cm
b = 14 cm
c = 15 cm

Solution:

S = \sqrt{s (s - a) (s - b) (s - c)} = 84 s = (a + b + c) / 2 = (3 x + 3) / 2 = 1.5 x + 1.5 (1.5 x + 1.5) (1.5 x + 1.5 - x) (1.5 x + 1.5 - x - 1) (1.5 x + 1.5 - x - 2) = 8 4^{2} (1.5 x + 1.5) (0.5 x + 1.5) (0.5 x + 0.5) (0.5 x - 0.5) = 7056 0.1875 x^{4} + 0.75 x^{3} + 0.375 x^{2} - 0.75 x - 7056.56 = 0 x = 13 a = x = 13 cm

b = 13 + 1 = 14 cm

c = 13 + 2 = 15 cm

Equation is non-linear.

Equation is not quadratic.

Equation is not cubic.

The real roots of the equation:

x₁ = -14.9999987727
x₂ = 12.9999987727

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