Question

In triangle DEF ,angle L =90⁰ EN is perpendicular to DF .DN =5cm DF=45cm then DE=___ ​

Answer 1

Given : In triangle DEF ,angle E =90⁰ EN is perpendicular to DF .DN =5cm DF=45cm

To Find : DE ​

Solution:

∠DNE = ∠ENF

∠EDN = ∠FEN     ( 90° - F)

∠DEN = ∠EFN        ( 90° - D)

ΔDNE ≈ Δ ENF

=> DN/EN  = EN/FN

FN = DF - FN = 45 - 5 = 40 cm

=> 5/EN  = EN/40

=> EN² = 200

=> EN = 10√2

DE²  = DN² + EN²

=> DE² = 5² + 200

=> DE² = 225

=> DE = 15  cm

DE = 15  cm  

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