Final answer:
The length of segment CD, given that AB and CD are congruent and their expressions are 5x and 3x + 10 respectively, is found to be 25 units after solving the equation 5x = 3x + 10 for 'x' and substituting it back into CD's expression.
Step-by-step explanation:
The question asks to find the length of segment CD given two segments, AB and CD, which are congruent. This means that their lengths are equal. The length of AB is given as 5x and CD is 3x + 10. To find the length of CD, we set these two expressions equal to each other to solve for 'x' and then substitute 'x' back into the expression for CD.
Setting the expressions equal to each other yields the equation:
5x = 3x + 10.
Solving for 'x' involves:
Subtracting 3x from both sides, which gives us 2x = 10.
Dividing both sides by 2, we find that x = 5.
Now we know the value of x, we can find the length of CD by substituting 'x' back into CD's expression:
CD = 3x + 10 = 3(5) + 10 = 15 + 10 = 25.
Therefore, the length of segment CD is 25 units.