Question

CAN SOMEONE PLEASE SOLVE THIS?????????? NEED HELP!!!!!!!!!!!!!!!!!!!

Answer 1

x = 9, GH = 21, CD = 17

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.

`\therefore \: GH = (1)/(2) (CD + FE) \\ \\ \therefore \:3x - 6 =(1)/(2) (2x - 1 + 25) \\ \\ \therefore \:3x - 6 =(1)/(2) (2x + 24) \\ \\ \therefore \:3x - 6 =(1)/(2) * 2 (x + 12) \\ \\ \therefore \:3x - 6 = x + 12 \\ \\ \therefore \:3x - x = 12 + 6 \\ \\ \therefore \:2x = 18 \\ \\ \therefore \:x = (18)/(2) \\ \\ \huge\red{ \boxed{\therefore \:x = 9}} \\\\ \because \overline{GH} = 3x - 6 \\ \\\therefore \:\overline{GH} =3 * 9 - 6 \\ \\ \therefore \:\overline{GH} =27 - 6 \\ \\ \huge\purple{ \boxed{\therefore \:\overline{GH} =21}} \\ \\ \because\overline{CD} = 2x - 1 \\\\ \therefore \:\overline{CD} =2 * 9 - 1 \\ \\ \therefore \:\overline{CD} =18 - 1 \\ \\ \huge\pink{ \boxed{\therefore \:\overline{CD} =17}} \\ \\`