Answer:
x = 3.51
Step-by-step explanation:
Since, formula to determine the area f a triangle is,
Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
8 = [tex]\frac{1}{2}(x + 1)(3x - 7)[/tex]
16 = x(3x - 7) + 1(3x - 7)
16 = 3x² - 7x + 3x - 7
16 = 3x² - 4x - 7
0 = 3x² - 4x - 23
3x²- 4x - 23 = 0
By quadratic formula,
x = [tex]\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
x = [tex]\frac{4\pm \sqrt{(-4)^{2}-4(3)(-23)}}{2(3)}[/tex]
x = [tex]\frac{4\pm \sqrt{292}}{6}[/tex]
x = [tex]\frac{4\pm 17.09}{6}[/tex]
x = 3.51, -2.18
But the length of sides can't be negative.
Therefore, x = 3.51 will be the answer.
