Exact Answer: x = 16/3
Approximate Answer: x = 5.333
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Work Shown:
base = 3x-1
height = x
area of triangle = (base*height)/2
40 = x*(3x-1)/2
40*2 = 3x^2 - x
80 = 3x^2 - x
0 = 3x^2 - x - 80
3x^2 - x - 80 = 0
Now apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-80)}}{2(3)}\\\\x = \frac{1\pm\sqrt{961}}{6}\\\\x = \frac{1\pm31}{6}\\\\x = \frac{1+31}{6} \ \text{ or } \ x = \frac{1-31}{6}\\\\x = \frac{32}{6} \ \text{ or } \ x = \frac{-30}{6}\\\\x = \frac{16}{3} \ \text{ or } \ x = -5\\\\x \approx 5.333 \ \text{ or } \ x = -5\\\\[/tex]
A negative height doesn't make sense, so we ignore x = -5
The only solution is x = 16/3 which approximates to x = 5.333
