Question

Find the value for x. Round your answer to the nearest hundredth. Area of the triangle = 8 ft^2​

Answer 1

Answer:

x = 3.51

Step-by-step explanation:

Since, formula to determine the area f a triangle is,

Area = $\frac{1}{2}(\text{Base})(\text{Height})$

     8 = $\frac{1}{2}(x + 1)(3x - 7)$

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 = $\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

x = $\frac{4\pm \sqrt{(-4)^{2}-4(3)(-23)}}{2(3)}$

x = $\frac{4\pm \sqrt{292}}{6}$

x = $\frac{4\pm 17.09}{6}$

x = 3.51, -2.18

But the length of sides can't be negative.

Therefore, x = 3.51 will be the answer.