Question

100 Points for this Question. PLEASE HELP ASAP.

Answer 1

`\\ \rm\Rrightarrow (AB)/(AD)=(BC)/(CD)`

`\\ \rm\Rrightarrow (18)/(x)=(19)/(11)`

`\\ \rm\Rrightarrow 19x=198`

`\\ \rm\Rrightarrow x=10.4`

Answer 2

x = 10.4 (nearest tenth)

Explanation:

Angle Bisector Theorem

The angle bisector of any angle in a triangle will divide the side opposite the bisected angle in the ratio of the sides containing the angle.

Therefore:

AD : DC = BA : BC

Given:

• AD = x
• DC = 11
• BA = 18
• BC = 19

Substituting the given values into the ratio and solving for x:

`\implies \sf x : 11 = 18 : 19`

`\implies \sf (x)/(11)=(18)/(19)`

`\implies \sf 19x=18 \cdot 11`

`\implies \sf 19x=198`

`\implies \sf x=(198)/(19)`

`\implies \sf x=10.4 \: (nearest\:tenth)`