Answer:
x = 9, GH = 21, CD = 17
Step-by-step explanation:
Quadrilateral CDEF is a trapezoid in which G and H are mid points of the sides CF and DE respectively.
In a trapezoid, segment joining the mid points is equal to the half of the sum of the parallel sides.
[tex] \therefore \: GH = \frac{1}{2} (CD + FE) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =\frac{1}{2} (2x + 24) \\ \\ \therefore \:3x - 6 =\frac{1}{2} \times 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = \frac{18}{2} \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 \times 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 \times 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\ [/tex]
