Q7 of 45 Page 38

In figure 2.21, ∠DEF = 90°, FG ⊥ ED, If GD = 8, FG = 12,find (1) EG (2) FD and (3) EF

In ∆DGF, ∠DGF = 900


FD2 = DG2 + GF2


⇒ FD2 = 64 + 144


⇒ FD2 = 208


FD =


In ∆DEF, ∠DFE = 900


ED2 = DF2 + EF2


⇒ (EG + 8)2 = 208 + EF2 … (1)


In ∆EGF, ∠FGE = 900


EF2 = EG2 + GF2


⇒ (EG + 8)2 – 208 = EG2 + 144


⇒ EG2 + 2.EG.8 + 64 – 208 = EG2 + 144


EG = 18


From (1)


⇒ (EG + 8)2 = 208 + EF2


EF = 6√13.


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