Final answer:
Using the Pythagorean theorem, the length of segment CD in right triangle ADC is calculated to be 4 units, which is not included in the given answer choices. It suggests an error in the question details or the options provided.
Step-by-step explanation:
To find the length of segment CD in triangle ADC, we can make use of the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. From the problem statement, we know that triangle ABC is a right triangle with a right angle at B, and the lengths of AC and AB are 7 units and 4 units, respectively. Because DC is parallel to AB and triangle ADC is also a right triangle with a right angle at A, triangles ABC and ADC share the side AC, which means that AC is also the hypotenuse for triangle ADC.
Applying the Pythagorean theorem to triangle ADC:
CD2 + AC2 = AD2
Since AC is shared and its length is 7 units, AD would be the hypotenuse of triangle ABC and can be calculated as:
AD2 = AB2 + AC2 = 42 + 72 = 16 + 49 = 65
Thus, AD = √65. Now substitute the value back into the first equation:
CD2 + 72 = (√65)2
CD2 + 49 = 65
CD2 = 65 - 49
CD2 = 16
CD = √16
CD = 4 units
Therefore, the length of segment CD is 4 units, which is not one of the options provided in the multiple-choice answers. There might be a mistake in either the problem statement or the options given.