Answer : The value of side DE is, 15 m
Step-by-step explanation :
First we have to determine the side DF.
Using Pythagoras theorem in ΔDFC :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](CD)^2=(DF)^2+(CF)^2[/tex]
Given:
Side CD = 8 m
Side CF = 17 m
Now put all the values in the above expression, we get the value of side DF.
[tex](8)^2=(DF)^2+(17)^2[/tex]
[tex]DF=\sqrt{(17)^2-(8)^2}[/tex]
[tex]DF=15m[/tex]
Now we have to determine the value of side DE.
Side DE = Side DF = 15 m (By congruent triangle DFB and DEB)
The ΔDFB and ΔDEB are congruent triangles.
Proof:
Side DB = Side DB (common side)
∠DBE = ∠DBF (BD is angle bisector, so these angle are always equal)
∠E = ∠F (equal to 90°)
ΔDFB ≅ ΔDEB (By SAS congruency)
So, Side DE = Side DF
Hence, the value of side DE is, 15 m
