Question

Question 5
What is the value of x?

Answer 1

x = 27

Explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

`(x+8)/(10)=(2x-5)/(14)` cross multiply

`14(x+8)=10(2x-5)` use the distributive property

`(14)(x)+(14)(8)=(10)(2x)+(10)(-5)`

`14x+112=20x-50` subtract 112 from both sides

`14x=20x-162` subtract 20x from both sides

`-6x=-162` divide both sides by (-6)

`x=27`