Question

plzzzz solve my question step by step with (pythagoras theorem)

Answer 1

${\huge{\mathfrak{\red{G}{iven}}}}$

D is the mid-point of BC

Therefore, DC = BC/2

${\huge{\mathfrak{\red{T}{o\:prove}}}}$

${AB^2 = 4AD^2 -3AC^2}$

${\huge{\mathfrak{\red{B}{rainliest\:answer}}}}$

Now, in Triangle ABC,

${AB^2 = AC^2 + BC^2}$........(1)

(Pythagoras theorem)

Now, In Triangle ADC,

${AD^2 = AC^2 + DC^2}$

(Pythagoras theorem)

NOW, ${AD^2 = AC^2 + {(BC/2)}^2}$

${AD^2 = AC^2 + BC^2/4}$

${4AD^2 = 4AC^2 + BC^2}$......(2)

Subtract (2) from (1)

${AB^2 = AC^2 + BC^2}$

${4AD^2= 4AC^2 + BC^2}$

(--)

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${AB^2 - 4AD^2 = -3AC^2 }$

${AB^2 = 4AD^2 - 3AD^2}$

Hence proved.

${\huge{\mathfrak{Be\:Brainly}}}$