Answer:
The value of x is 25.
Step-by-step explanation:
Given:
side AB = [tex]3x-5[/tex]
side BC = [tex]2x+20[/tex]
side AC = [tex]4x-30[/tex]
In Δ ABC is an equilateral triangle.
In equilateral triangle all three angles are same and also the sides are same.
Hence side AB = side BC
Substituting the values for side AB and side BC we get,
[tex]3x-5=2x+20\\3x-2x=20+5\\x=25[/tex]
Hence the value of x = 25.
Answer:
The value of x for the given figure is 95 And 1.67
Step-by-step explanation:
From Given figure :
Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex]
or , Sin C = [tex]\dfrac{\textrm 3x - 5}{\textrm 4 x - 30}[/tex]
Cos angle = [tex]\dfrac{\textrm Base}{\textrm Hypotenuse}[/tex]
or , Cos C = [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex]
Or, Cos c = [tex]\sqrt{1 - sin^{2}C }[/tex]
Or, [tex]\dfrac{\textrm 2x + 20}{\textrm 4 x - 30}[/tex] = [tex]\sqrt{1-(\frac{3x - 5}{4 x + 20} })^{2}[/tex]
or, [tex](\frac{2x+20}{4x-30}) ^{2}[/tex] = 1 - [tex](\frac{3x-5}{4x-30} )^{2}[/tex]
[tex]\frac{4x^{2}+400+80x}{16x^{2}+900-240x}[/tex]= 1- ( [tex]\frac{9x^{2}+25-30x}{16x^{2}+900-240x}[/tex] )
Or, 4x²+400+80x = [tex]16x^{2}+900-240x[/tex] - 9x² -25 +30x
or, 4x²+400+80x = 7 x² + 875 -210x
or, 3 x² + 475 -290 x = 0
Or, Solving the equation
3 x² - 285 x - 5 x + 475 = 0
or, 3 x ( x - 95 ) - 5 ( x - 95 ) = 0
or, ( x - 95 ) ( 3 x - 5 ) = 0
∴ x = 95 and x = 1.67
Hence The value of x for the given figure is 95 And 1.67 Answer
