Find the length of AB .

Question

asked Jan 1, 2024 189k views

1 Answer

ZassX · Answer 1 · 2024-01-05T02:25:20+0000

Answer:

AB = 7.2

Explanation:

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:

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

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

$\implies \sf AB=7.2$