Question

What is the value of x?



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x =

Answer 1

The value of x is 25.

Explanation:

Given:

side AB =
`3x-5`

side BC =
`2x+20`

side AC =
`4x-30`

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,

`3x-5=2x+20\\3x-2x=20+5\\x=25`

Hence the value of x = 25.

Answer 2

The value of x for the given figure is 95 And 1.67

Explanation:

From Given figure :

Sin angle =
`(\textrm perpendicular)/(\textrm Hypotenuse)`

or , Sin C =
`(\textrm 3x - 5)/(\textrm 4 x - 30)`

Cos angle =
`(\textrm Base)/(\textrm Hypotenuse)`

or , Cos C =
`(\textrm 2x + 20)/(\textrm 4 x - 30)`

Or, Cos c =
`\sqrt{1 - sin^(2)C }`

Or,
`(\textrm 2x + 20)/(\textrm 4 x - 30)` =
`\sqrt{1-((3x - 5)/(4 x + 20) })^(2)`

or,
`((2x+20)/(4x-30)) ^(2)` = 1 -
`((3x-5)/(4x-30) )^(2)`

`(4x^(2)+400+80x)/(16x^(2)+900-240x)`= 1- (
`(9x^(2)+25-30x)/(16x^(2)+900-240x)` )

Or, 4x²+400+80x =
`16x^(2)+900-240x` - 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