Sides of the triangle

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

Correct answer:

a =  13 cm
b =  14 cm
c =  15 cm

Step-by-step explanation:

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

$b=13+1=14\text{ cm}$

$c=13+2=15\text{ cm}$

Equation is non-linear.

Equation is not quadratic.

Equation is not cubic.

The real roots of the equation:

x₁ = -14.999998772705
x₂ = 12.999998772705

Our simple equation calculator calculates it.

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