in triangle DEF
seg DG perpendicular to side EF and EG:GF= 1:2
prove that :
Ef²= 3 (DFsquare - DEsquare)
Answers
Given : in triangle DEF seg DG perpendicular to side EF
EG:GF= 1:2
To Find : prove that :
EF²= 3 (DF² - DE²)
Solution:
DG² = DE² - EG²
DG² = DF² - FG²
Equate DG²
DE² - EG² = DF² - FG²
=> DF² - DE² = FG² - EG²
EG:GF= 1:2
=> FG = 2EG
=> DF² - DE² = (2EG)² - EG²
=> DF² - DE² = 4 EG ² - EG²
=> DF² - DE² = 3 EG²
EF² = (EG + FG)²
=> EF² = (EG + 2EG)²
=> EF² = (3EG)²
=> EF² =9EG²
=> EF² =3.3EG²
=> EF² =3 (DF² - DE²)
QED
Hence proved
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