Question

From the figure x= ​

Answer 1

Answer:

x = 15

Step-by-step explanation:

All use of Pythagoras Theorem is here..

Answer 2

Answer:

x = 15

Step-by-step explanation:

Your first person, who gave you the explanation, went trough the prove that the segment AD which divide right angled Δ into two right angled Δs is geometric mean AD² = BD×DC  

If you know that, then there is shorter way for you:

From ΔABC: AD² = 5x  ..... (1)

From ΔADC: AD² = (10√3)² - x² ...... (2)

Use substitution method for (1) and (2)

5x = 300 - x²

x² + 5x - 300 = 0

D = 5² - 4×(- 300) = 35²

$x_{12}$ = (- 5 ± 35) ÷ 2

$x_{1}$ = - 20 (NOT a solution for our task)

$x_{2}$ = 15