Answer:
x = 3
Step-by-step explanation:
Let the altitude from B to AC intersect at point D. Then BD is a height of the triangle with base AC
ΔABD is a 30-60-90 triangle since m∠A = 30
Therefore, AB = 2(BD) or BD = AB/2 = (x+3)/2
Area of the triangle = bh/2 = AC(BD)/2 = 4x(x + 3)/(2)(2)
= x(x + 3) = 18
[tex]x^{2} + 3x = 18[/tex]
[tex]x^{2} + 3x - 18 = 0[/tex]
(x + 6)(x - 3) = 0
x = -6 or x = 3
x cannot equal -6, so x = 3
In this exercise we have to use the knowledge of triangle to calculate the value of X, in this way we find that:
[tex]X=3[/tex]
In this way, we can write the treated area of the triangle as:
[tex]bh/2 = AC(BD)/2 = 4x(x + 3)/(2)(2)\\=x(x + 3) = 18\\x^2+3x=18\\x^2+3x-18=0\\(x+6)(x-3)=0\\x=-6 \ or \ x=3[/tex]
See more about triangle at brainly.com/question/25813512
