Question

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

Answer 1

x = 3.51

Explanation:

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

Area =
`(1)/(2)(\text{Base})(\text{Height})`

8 =
`(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 =
`(4\pm √(292))/(6)`

x =
`(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.