Answer:
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
