Final answer:
To find the numerical length of CD when point C is on line segment BD, we express BD as the sum of BC and CD. By setting up and solving the equation x + 4 + 5x = 5x + 7, we determine x to be 7 and thus, the numerical length of CD is 35 units.
Step-by-step explanation:
Since point C is on line segment BD, we can express BD as the sum of BC and CD. The problem states that BC equals x + 4, CD equals 5x, and BD equals 5x + 7. To find the numerical length of CD, we can set up the equation x + 4 + 5x = 5x + 7 since BD is the sum of BC and CD.
Solving for x, we get:
Combine like terms on each side: x + 5x = 5x and 4 = 7
This simplifies to 6x = 5x + 7
Subtract 5x from both sides: x = 7
Now that we have the value for x, we can find the numerical length of CD by substituting x into 5x:
CD = 5(7)
CD = 35
Therefore, the numerical length of CD is 35 units.