Answer:
DE = 26
Explanation:
We can find the length of the line segment DE by:
- solving for x
- plugging that x-value into the definition of DE in terms of x
We are given the following definitions in terms of x for the line segments CD and DE:
We also know that CD is the same length as DE because of the congruence marks. Therefore, to solve for x, we can equate their definitions in terms of x.
CD = DE
↓ substituting in their definitions in terms of x
2x + 7 = 4(x - 3)
↓ applying the distributive property to the right side ... a(b + c) = ab + ac
2x + 7 = 4x - 12
↓ subtracting 2x from both sides
7 = 2x - 12
↓ adding 12 to both sides
19 = 2x
↓ dividing both sides by 2
x = 9.5
Now, we can plug this x-value into the definition of DE in terms of x to solve for its length.
DE = 4(x - 3)
↓ plugging in 9.5 for x
DE = 4(9.5 - 3)
↓ executing the subtraction inside the parentheses
DE = 4(6.5)
↓ executing the multiplication
DE = 26