Question

What is the value of x?

Answer 1

$\bold{Answer :}$

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By applying Pythagoras theorem on triangle ABC, we get

AB² + AC² = BC²

or, x² + AC² = 6²

or, AC² = 36 - x²

Applying Pythagoras theorem on triangle ACD, we get

AD² + DC² = AC²

or, AD² + 3² = 36 - x²

or, AD² = 36 - 9 - x²

or, AD² = 27 - x²

Again, applying Pythagoras theorem on triangle ABD, we get

AD² + BD² = AB²

or, 27 - x² + 3² = x²

or, 2x² = 27 + 9

or, 2x² = 36

or, x² = 18

or, x = 3√2, taking the positive value

Therefore, the value of x is 3√2 units

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