Answer:
x = 3.08
Step-by-step explanation:
Construct a perpendicular AD from point A to opposite side BC,
By sine ratio,
sin(45)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}= \frac{AD}{(x+2)}[/tex]
AD = [tex]\frac{x+2}{\sqrt{2}}[/tex]
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(BC)(AD)[/tex]
[tex]4\sqrt{2}=\frac{1}{2}(2x-3)\frac{(x+2)}{\sqrt{2} }[/tex]
(2x - 3)(x + 2) = 16
2x(x + 2) - 3(x + 2) = 16
2x² + 4x - 3x - 6 = 16
2x² + x - 6 = 16
2x² + x - 22 = 0
By using quadratic formula,
x = [tex]\frac{-1\pm\sqrt{(1)^{2}-4(2)(-22)}}{2(2)}[/tex]
x = [tex]\frac{-1\pm\sqrt{177}}{4}[/tex]
x = 3.076, -3.576
x ≈ 3.08, -3.58
But length of the sides can't be negative
Therefore, x = 3.08 will be the answer.
