Question

If you solve this Question You are Legend In Mathematics​

Answer 1

$\sf\underline{From ∆ADC}$

$→\sf\pink{x² + (AD)² = (10√3)²}$

$→\sf\pink{\fbox{x² + (AD)² = 300}}$ ••••• (i)

$\sf\underline{From ∆ABC}$

$→\sf\blue{(AB)² + (10√3)² = (x+5)² }$

$\sf\blue{\fbox{(AB)² + 300 = (x+5)²}}$ ••••• (ii)

$\sf\underline{From ∆ABD}$

$→\sf\green{(5)² + (AD)² = (AB)² }$

$→\sf\green\fbox{25 + (AD)² = (AB)² }$ ••••• (iii)

$\sf\underline{Now, Solving\: equation \:(i)}$

$\sf\blue{x² + (AD)² = 300}$

$\sf\blue{x² + (AB² - 25) = 300}$ { From equ. (iii) }

$\sf\blue{x² + (x+5)² - 300 - 25 = 300}$ { From equ. (ii) }

$\sf\blue{x² + x² + 25 + 10x - 300 - 25 = 300}$

$\sf\blue{2x² + 10x - 600 = 0}$

$\sf\blue{x² + 5 x - 300 = 0}$

$\sf\blue{x² + 20x - 15x - 300 = 0}$

$\sf\blue{x(x+20) - 15 ( x+20) = 0}$

$\sf\blue{(x-15) ( x+20) = 0}$

$\sf\red{If x-15 = 0}$

$\sf\fbox\orange{x = 15}$

$sf\red[If x +20 = 0}$

$\sf\fbox\orange{x = -20}$

$\sf\yellow{\:\:\:\:\:\:\:--- Neglected}$

Answer 2

Answer:

hey here is ur answer in above pics

pls mark it as brainliest