Question

Please help me find the value of x!

Answer 1

Exact Answer: x = 16/3

Approximate Answer: x = 5.333

=======================================================

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

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(-1)\pm√((-1)^2-4(3)(-80)))/(2(3))\\\\x = (1\pm√(961))/(6)\\\\x = (1\pm31)/(6)\\\\x = (1+31)/(6) \ \text{ or } \ x = (1-31)/(6)\\\\x = (32)/(6) \ \text{ or } \ x = (-30)/(6)\\\\x = (16)/(3) \ \text{ or } \ x = -5\\\\x \approx 5.333 \ \text{ or } \ x = -5\\\\`

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