Question

In Triangle Abc,A-M-B,A-N-C And Mn || Bc. If Am=3X-1,Mb=2X+1,An=3X+1 And Nc=5X+1, Find Value Of X

Answer 1

Given :-

• in ∆ABC, MN || BC.
• AM = (3x - 1) .
• MB = (2x + 1) .
• AN = (3x + 1).
• NC = (5x + 1) .

To Find :-

• find the value of x ?

Solution :-

we know that,

• If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
• MN || BC .
• AM/MB = AN/NC .

Putting all values we get :-

→ (3x - 1)/(2x + 1) = (3x + 1)/(5x + 1)

→ (3x - 1)(5x + 1) = (3x + 1)(2x + 1)

→ 15x² + 3x - 5x - 1 = 6x² + 3x + 2x + 1

→ 15x² - 6x² - 5x - 2x - 1 - 1 = 0

→ 9x² - 7x - 2 = 0

→ 9x² - 9x + 2x - 2 = 0

→ 9x(x - 1) + 2(x - 1) = 0

→ (9x + 2)(x - 1) = 0

→ x = (-2/9) and 1.

since negative value of x is not possible.

Therefore,

value is x is equal to 1.

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