Answer:
The length of segment DC is 33 units.
Step-by-step explanation:
A perpendicular bisector of line segment divides the line into two equal parts at 90°.
This implies that the perpendicular bisector of line segment AC at B divides the line Ac into two equal parts AB and BC.
It is given that:
BC = 23 units
AB = 2x + 7 units
AD = 4x + 1 units
The measure of AB is 23 units, according to the perpendicular bisector definition.
Compute the value of x as follows:
AB = 2x + 7
23 = 2x + 7
2x = 23 - 7
2x = 16
x = 8 units
Then the measure of side AD is:
AD = 4x + 1
= 4 × 8 + 1
= 32 + 1
= 33 units
Consider the diagram below.
Consider the right-angled triangle ABD.
Use Pythagoras theorem to compute the length of DB² as follows:
[tex]AD^{2}=DB^{2}+AB^{2}\\\\33^{2}=DB^{2}+23^{2}\\\\DB^{2}=560[/tex]
Consider the right angles triangle DBC.
Use Pythagoras theorem to compute the length of DC² as follows:
[tex]DC^{2}=DB^{2}+BC^{2}\\\\=560+23^{2}\\\\=560+529\\\\=1089\\\\DC=\sqrt{1089}\\\\=33[/tex]
Thus, the length of segment DC is 33 units.
