Answer:
[tex]UV=8\ units[/tex]
[tex]XY=16\ units[/tex]
[tex]TW=24\ units[/tex]
Step-by-step explanation:
we know that
In this problem
XY is the mid-segment of trapezoid TUVW (because K is the midpoint segment TU and Y is the midpoint segment VW)
Remember that the length of the mid-segment is the sum of the two parallel bases divided by 2
so
[tex]XY=\frac{UV+TW}{2}[/tex]
substitute the given values
[tex]3x+7=\frac{3x-1+8x}{2}[/tex]
solve for x
Multiply by 2 both sides
[tex]6x+14=11x-1[/tex]
[tex]11x-6x=14+1[/tex]
[tex]5x=15[/tex]
[tex]x=3[/tex]
Find the length segment UV
[tex]UV=3x-1[/tex]
substitute the value of x
[tex]UV=3(3)-1=8\ units[/tex]
Find the length segment XY
[tex]XY=3x+7[/tex]
substitute the value of x
[tex]XY=3(3)+7=16\ units[/tex]
Find the length segment TW
[tex]TW=8x[/tex]
substitute the value of x
[tex]TW=8(3)=24\ units[/tex]
