Given the line segment BE
As shown:
BC = 3x + 47
CD = y
BD = x + 27
CE = x + 26
DE = 10
To find the length of BE, we will find the values of x and y
So,
[tex]\begin{gathered} y=BD-BC \\ y=(x+27)-(3x+47) \\ y=-2x-20\rightarrow(1) \\ y=x+26-10 \\ y=x+16\rightarrow(2) \end{gathered}[/tex]
Solve the equations (1) and (2) for x
[tex]\begin{gathered} x+16=-2x-20 \\ x+2x=-20-16 \\ 3x=-36 \\ x=-\frac{36}{3}=-12 \end{gathered}[/tex]
Substitute at (2) to find y
[tex]y=x+16=-12+16=4[/tex]
The length of BE = BC + CD + DE
[tex]BE=(3x+47)+y+10[/tex]
Substitute with x and y:
[tex]\begin{gathered} BE=3\cdot-12+47+4+10 \\ BE=25 \end{gathered}[/tex]
So, the answer will be ⇒ BE = 25
