Question

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Answer 1

Step-by-step explanation:

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

Hope it helps you!!

Answer 2

Step-by-step explanation:

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