Question

What is the value of x to the nearest tenth? The figure is not drawn to scale. (Also if anyone has any other answers from this I could use the help)

Answer 1

Solve this problem using the angle bisector theorem. This theorem states that when given a triangle with an angle bisector (line that cuts one of the angles in half, into two of the same angles), that angle bisector divides the opposite side into two segment proportional to the sides of the triangle (see image).

For our problem:
Using the angle bisector theorem, you can see that:

`\frac{6.3\: \text{(length of bottom segment)}}{5.4\: \text{(length of top segment)}} = \frac{11.2\: \text{(length of bottom side)}}{x\: \text{(length of top side)}}`

Now solve that proportion for the value of x:

`(6.3)/(5.4) = (11.2)/(x) \\ 6.3x = 11.2(5.4)\\ 6.3x = 60.48\\ x = (60.48)/(6.3) \\ x = 9.6`

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Answer: x = 9.6