Hi there!
[tex]\large\boxed{UV = 13}[/tex]
Since U and V are midpoints of the legs, then UV is the average of both WX and ZY.
Therefore:
(ZY + WX)/2 = UV
Substitute in the given expressions:
[(6x + 5) + (x + 7)]/2 = 8x - 3
Simplify by combining like terms:
(7x + 12)/2 = 8x - 3
Multiply both sides by 2:
7x + 12 = 16x - 6
Subtract 7x from both sides and add 6 to both sides:
18 = 9x
Divide both sides by 9:
18/9 = x
x = 2.
Plug in this value of x into the equation for UV:
8(2) - 3 = 16 - 3 = 13.
