In the trapezoidal ABCD, ab = 8, ad = 5, CD = 6, BC = 15. Point E is on the bottom BC, and point F is on the waist CD. EF bisects the area and perimeter of ABCD at the same time to find the length of CE

In the trapezoidal ABCD, ab = 8, ad = 5, CD = 6, BC = 15. Point E is on the bottom BC, and point F is on the waist CD. EF bisects the area and perimeter of ABCD at the same time to find the length of CE

The triangle ABG is a right triangle whose three sides are 6, 8 and 10 respectively. The height of the triangle (also trapezoid) is 4.8, the area of the trapezoid is 48 and the perimeter is 34
Let X be the length of CE, then
X*4.8*（17-X）/6*1/2=24
The solution is x = 12 or 5
But 5 does not satisfy the topic meaning to give up, therefore CE long 12