The value of x is √1037.Therefore, option √1037 is correct.
The Pythagorean theorem can be used to solve this problem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Value of x = BC + CD
In this case, we can use the Pythagorean theorem on triangle ACD
29^2 = 12^2 + AD^2
841 = 144 + AD^2
AD^2 = 841 -144
AD^2 = 697
AD = √697
In this case, we can use the Pythagorean theorem on triangle ABC
14^2 = 12^2 + BC^2
196 = 144 + BC^2
BC= √52
We can then solve for x by taking the square root of both sides of the equation.
x = √52 + √697
x = 7.21 + 26.4
x = 33.61
33.61 Approximately = √1037
Therefore, the value of x is √1037.