The value of x is 10.5
Solution:
Given RST is a triangle.
BC bisect the triangle RST.
SC = CR and SB = BT
This implies that BC is the mid-segment of ΔRST.
By mid-segment theorem:
Mid-segment = Half of the parallel side
[tex]$BC = \frac{1}{2}\times RT[/tex]
[tex]$1.5x-5 = \frac{1}{2}\times (x+11)[/tex]
Multiply by 2 on both sides.
[tex]$2\times(1.5x-5) =2\times \frac{1}{2}\times (x+11)[/tex]
[tex]$3x-10 = x+11[/tex]
Add 10 on both sides.
[tex]$3x-10 +10= x+11+10[/tex]
[tex]$3x= x+21[/tex]
Subtract x from both sides.
[tex]$3x-x= x+21-x[/tex]
[tex]$2x=21[/tex]
Divide by 2 on both sides.
[tex]$\frac{2x}{2} =\frac{21}{2}[/tex]
x = 10.5
The value of x is 10.5
