Answer:
The length of RS is 47 units
Step-by-step explanation:
Midsegment Theorem
The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides.
The length of the midsegment of a trapezoid is the average of the lengths of the bases.
The midsegment of the given trapezoid is VW, and the bases are RS and UT.
According to the midsegment theorem:
[tex]\displaystyle VW=\frac{RS+UT}{2}[/tex]
Substituting the variable lengths of the sides:
[tex]\displaystyle 3x+5=\frac{2x+15+6x-37}{2}[/tex]
Operating:
[tex]\displaystyle 3x+5=\frac{8x-22}{2}[/tex]
Dividing the fraction:
[tex]3x+5=4x-11[/tex]
Rearranging:
[tex]4x-3x=5+11[/tex]
Operating:
x=16
The length of RS is:
[tex]RS=2x+15=2*16+15=32+15=47[/tex]
The lenght of RS is 47 units
