Question

AD¯¯¯¯¯ , BD¯¯¯¯¯ , and CD¯¯¯¯¯ are angle bisectors of the sides of △ABC . CF=8 m and CD=17 m.

Answer 1

Answer: DE= 15 m

Explanation:

Since, in $\triangle CDF$,

After applying, Pythagoras theorem, $DF^2=CD^2-CF^2=(17)^2-(8)^2=289-64=225$

Thus, $DF^2=225 \Rightarrow DF=\sqrt{225} \Rightarrow DF=15$ m

Again, in $\triangle BDF$ and $\triangle BDE$,

$\angle BED= \angle BFD$ ( Right angles)

BD=BD ( common edges)

$\angle DBE= \angle DBF$ (BD makes the angle bisector of angle B.)

Thus, according to AAS condition- $\triangle BDF\cong \triangle BDE$

So, DE=DF (CPCT)

Therefore, DE=DF=15m⇒DE=15 m

Answer 2

To solve this you have to use the Pythagorean Theorem. 
Which is a²+b²=c²
CF,CD,and DF makes a triangle 
Substitute it in
a²+8²=17² Add
a²+64=289 Subtract 64 to get a alone
a²=225 Square root it 
a=15