Question

45 Points!! Please help me with this question!

Answer 1

If P is the midpoint of DE, then DE = DP + PE and DP = PE.

Therefore DE = 2DP.

We have DP = 3x + 2 and DE = 10x - 12.

The equation:

10x - 12 = 2(3x + 2)       use distributive property

10x - 12 = (2)(3x) + (2)(2)

10x - 12 = 6x + 4      add 12 to both sides

10x = 6x + 16       subtract 6x from both sides

4x = 16     divide both sides by 4'

x = 4

DP = 3x + 2 → DP = 3(4) + 2 = 12 + 2 = 14

Answer: DP = 14 units.