Question

Please solve this

find x based on figure​

Answer 1

Answer:

It's an interesting question :)

The main concept involved here is the knowledge of Pythagoras Theorem.

Let us consider AB = y and AD = z

Consider ΔABC,

Applying Pythagoras Theorem we get,

→ (10√3)²  + y² = (5+x)²

→ 300 + y² = ( x² + 10x + 25 )   ... ( 1 )

Consider ΔADC,

Applying Pythagoras Theorem we get,

→ z² + x² = (10√3)²

→ z² + x² = 300   ... ( 2 )

Consider ΔADB,

Applying Pythagoras Theorem we get,

→ 5² + z² = y²

→ 25 + z² = y²   ... ( 3 )

Subtracting ( 2 ) from ( 3 ) we get,

→ 25 + z² - z² - x² = y² - 300

→ 25 - x² = y² - 300

→ 300 - y² = x² - 25  ... ( 4 )

Now we have eliminated z².

Now adding ( 1 ) and ( 2 ) we get,

→ 300 - y² + 300 + y² = x² + 10x + 25 + x² - 25

→ 600 = 2x² + 10x

Dividing by 2 throughout the equation we get,

→ 300 = x² + 5x

→ x² + 5x - 300 = 0

Factorising the above equation we get,

→ x² + 20x - 15x - 300 = 0

→ x ( x + 20 ) -15 ( x + 20 ) = 0

→ ( x + 20 ) ( x - 15 ) = 0

→ x = 15 or x = -20

We cannot have a side to be negative.

Hence the value of x is 15.

Answer 2

Step-by-step explanation:

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