Question

As shown figure, ∠DFE = 90°, FG ⊥ ED, if GD = 8, FG = 12, then EG = ?

Answer 1

(i) In ∆DEF,

∠DFE = 90° and seg FG ⊥ hypotenuse ED  ...[Given]

∴ FG² = EG × GD      ......[By theorem of geometric mean]

∴ (12)² = EG × 8    ......[Given]

∴ 144 = EG × 8

∴ EG = `144/8`

∴ EG = 18 units

(ii)  In ∆DGF,

∠DGF = 90°                   .....[ ⸪ FG ⊥ ED]

∴ FD² = FG² + GD²      ......[Pythagoras theorem]

∴ FD² = (12)² + (8)²    ......[Given]

∴ FD² = 144 + 64

∴ FD² = 208

∴ FD = `sqrt(16 xx 13)`    ......[Taking square root of both sides]

∴ FD = `4sqrt(13)` units

(iii) In EGF,

 ∠EGF = 90°    ......[⸪ FG ⊥ ED]

∴ EF² = EG² + FG²    ......[Pythagoras theorem]

∴ EF² = (18)² + (12)²   ......[From (i) and given]

∴ EF² = 324 + 144

∴ EF² = 468

∴ EF = `sqrt(36 xx 13)`    .......[Taking square root of both sides]

∴ EF = `6sqrt(13)` units