Question

please solve it fast I need help right now please ​

Answer 1

HEY MATE HERE IS UR ANSWER WITH PROPER EXPLAINATION.....

GIVEN,

BD = DC

and angle ABC = 90°

TO PROVE = AC² = AD² + 3CD²

PROOF = IN ∆ ABC ,

BY PYTHAGOREAN THEORM ,

AC² = AB² + BC² ---------------------------(1)

NOW , IN ∆ ABD , BY PYTHAGOREAN THEORM,

AD² = AB² + BD²

=> AB² = AD² - BD²

=> AB² = AD² - DC² ----{SINCE , BD = DC] -----(2)

NOW , FROM EQ. 1

AC² = AB² + BC²

=> AC² = AB² + (BD + DC)²

=> AC² = AB² + (2DC)² ------{ SINCE, BD = DC]

SO, AC² = AB² + 4DC² -------------(3)

BY PUTTING EQ. 2 IN EQ.3

AC² = AD² -DC² + 4DC²

SO, AC² = AD² + 3DC²

HENCE PROVED.......

THANKS

PLZ MARK AS BRAINLIEST.........