Question

In the diagram, segment AD bisects angle BAC.

Given the following segment lengths, find the value of x.
Round to the nearest tenth.

AB: 31
AC: 23

Show all your work

Answer 1

x ≈ 11.5

Explanation:

AD is an angle bisector of ∠ BAC and divides the opposite side into segments that are proportional to the other two sides, that is

`(BD)/(CD)` =
`(AB)/(AC)` ( substitute values )

`(x)/(20-x)` =
`(31)/(23)` ( cross- multiply )

23x = 31(20 - x) ← distribute parenthesis

23x = 620 - 31x ( add 31x to both sides )

54x = 620 ( divide both sides by 54 )

x =
`(620)/(54)` ≈ 11.5 ( to the nearest tenth )