Question

As shown in figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, then (1) EG = ? (2) FD = ? (3) EF = ?

Answer 1

(1) 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

(2)  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

(3) 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