Find the value of x in the figure below. (picture included)

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

1,645,493,059.35

step-by-step explanation:

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step-by-step explanation:

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