Question

Find the length of AB .

Answer 1

AB = 7.2

Explanation:

Angle Bisector Theorem

An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

`\boxed{\sf (segment\;1)/(segment\;2)=(side\;1)/(side\;2)}`

In the given triangle ABC, AD bisects ∠BAC, so:

`\implies \sf (BD)/(DC)=(AB)/(AC)`

Substitute the given values and solve for AB:

`\implies \sf (4)/(10)=(AB)/(18)`

`\implies \sf (4 \cdot 18)/(10)=AB`

`\implies \sf AB=7.2`