Answer:
Therefore the length FG is 16 unit.
Explanation:
Given:
∠E ≅ ∠G = 90°
DF bisects ∠EDG
Bisector Divide the angle in EQUAL parts
∴∠EDF ≅ ∠GDF
FE = n +5
FG = 2n - 6
To Find:
FG = ?
Solution:
In ΔEDF and ΔGDF
∠E ≅ ∠G = 90° ……….{Given}
∠EDF ≅ ∠GDF ..……..{DF bisects ∠EDG}
DF ≅ DF ……….{Reflexive Property}
ΔEDF ≅ ΔGDF ….{ By Angle-Angle-Side Congruence test}
∴ FE ≅ FG .....{corresponding parts of congruent triangles are congruent}
Substituting the values of FE and FG we get

Substituting ' n ' in FG we get
Therefore the length FG is 16 unit.