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⚠️ Need help solving this pls! ⚠️

⚠️ Need help solving this pls! ⚠️-example-1
User Pickypg
by
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1 Answer

6 votes

Answer:

DE = 26

Explanation:

We can find the length of the line segment DE by:

  1. solving for x
  2. 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:

  • CD = 2x + 7
  • DE = 4(x - 3)

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

User Wishi
by
8.8k points