Question

What is the value of x? (not drawn to scale)

Answer 1

x = 15

Explanation:

Angle Bisector Theorem

The angle bisector of any angle in a triangle divides the side opposite the bisected angle into two parts proportional to the other two sides of the triangle.

From inspection of the given triangle, we can see that the angle between the sides labelled "x" and "25" has been bisected (divided into two equal parts).

Therefore, according to the Angle Bisector Theorem:

`\implies x:25=9:15`

`\implies (x)/(25)=(9)/(15)`

`\implies 25 \cdot (x)/(25)=25 \cdot (9)/(15)`

`\implies x=(225)/(15)`

`\implies x=15`