# Math Help - DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.

1. ## DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.

DEFG is a trapezoid, DH = GH, EI = FI, and HI = 15.5. Find the value of x.

A)13
B)12
C)15
D)14
E)16

2. If you imagine taking a copy of the trapezoid, flip it round 180 degrees and place the sloping edges together, you get a rectangle. Its long edge is DE + GF and that is the same as HI + IH = 2 HI = 31.

So now you have an equation:

$\left({\frac x 2 + 3}\right) + (2x - 12) = 31$

All you need to do is solve that equation.

3. Another way of looking at it: the length of the "midline" of a trapezoid is the average of the lengths of the two bases.

$\frac{\frac{x}{2}+ 3+ 2x-12}{2}= 15.5.$