Answer:
x ≈ 2.4
Step-by-step explanation:
Area of the triangle = 1/2 absin theta
Find the diagram of the triangle attached
a = 2x-3
b =x+2
theta = 45°
Substitute and find x
4√2 = 1/2(2x-3)(x+2)sin45
8/√2 = (2x-3)(x+2)(1/√2)
8 = (2x-3)(x+2)
Expand
8 = 2x²+4x-3x-6
2x²+x-6-8=0
2x²+x-14 = 0
x = -1±√1²-4(14)(2)/2(2)
x = -1±√1+112/4
x = -1±√113/4
x = -1+10.63/4
x = 9.63/4
x = 2.4
The value of x is 3.075.
Given that,
The area of the triangle is [tex]4\sqrt{2}[/tex] square meter,
and [tex]\theta[/tex] is 45 degrees.
The one side of the triangle is (2x-3) and the other side of the triangle is (x+2).
We have to determine
The value of x.
According to the question
The area of the triangle is determined by the following formula,
[tex]\rm Area \ of \ triangle = \dfrac{1}{2} sin\theta[/tex]
Substitute all the values in the formula
[tex]\rm Area \ of \ triangle = \dfrac{1}{2} absin\theta\\\\4\sqrt{2} = \dfrac{1}{2} (2x-3)(x+2) sin45\\\\2\times4\sqrt{2} = (2x^2+4x-3x-6)\dfrac{1}{\sqrt{2} }\\\\\sqrt{2} \times8\sqrt{2} = (2x^2+x-6)\\\\8\times2 = (2x^2+x-6)\\\\16 = 2x^2+x-6\\\\2x^2+x-6-16=0\\\\2x^2+x-22=0\\\\x = \dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\\\\x = \dfrac{-1\pm\sqrt{(-1)^2-4\times2\times(-22)} }{2\times2}\\\\x = \dfrac{-1\pm \sqrt{177} }{4}\\\\x = \dfrac{-`1\pm13.30 }{4}\\\\[/tex]
[tex]\rm x = \dfrac{-1+13.30}{4} \ and \ x = \dfrac{-1-13.30}{4} \\\\x = \dfrac{12.30}{4} \ and \ x= \dfrac{-14.30}{4}\\\\x = 3.075 \ and \ x = -3.575[/tex]
The value of x can not be negative so the value of x is 3.075.
Hence, The required value of x is 3.075.
For more details refer to the link given below.
https://brainly.com/question/15894203
