Final answer:
Setting the equations for the diagonals of the isosceles trapezoid equal to each other, we find that the value for v is 38.
Step-by-step explanation:
The question involves determining the value of v in an isosceles trapezoid, where the lengths of the non-parallel sides (diagonals) are FH=3v+38, and GI=2v+76. Since it is an isosceles trapezoid, these two diagonals are equal in length, therefore we can set the equations equal to each other to solve for v.
We get the equation 3v + 38 = 2v + 76. We solve for v by subtracting 2v from both sides, yielding v = 38. Hence, the value of v is 38.