Question

From the figure, x =​

Answer 1

Answer:

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Answer 2

Answer:

     x = 15 ⇒ (2)

Step-by-step explanation:

Let AB = z

Let AD = y

Pythagoras theorem - Hypotenuse² = Base² + Altitude²

y² = (x)² + (10√3)²

y² + x² =  300

y² = 300 - x²  -----{i}

z² = (y)² + (5)²

z² = y² + 25 ------{ii}

from {i} and {ii}

z² = x² + 300 + 25

z² = 325 - x²

(BC)² = (AB)² + (AC)²

(5 + x)² = z² + (10√3)²

25 + x² + 10x = 325 - x² + 300

25 + x² + 10x = 625 - x²

-600 + 2x² + 10x = 0

2x² + 10x - 600 = 0

2x² + 40x - 30x - 600 = 0

2x(x + 20) - 30(x + 20) = 0

(x + 20) (2x - 30) = 0

x = -20 , 2x = 30

x = -20 , x = 15

x cannot be a negative value

Hence x = 15 ⇒ (2)