Question

DEFG is an isosceles trapezoid with bases line FE and line GD. DE equals 2X +5, and FG equals 6X -7 find DE.

Answer 1

In an isosceles trapezoid, the lengths of the bases are equal. In this case, we have:

- Base FE (denoted as DE) = \( 2X + 5 \)
- Base GD (denoted as FG) = \( 6X - 7 \)

Since FE and GD are the bases of the trapezoid, we can set them equal to each other:

\[
2X + 5 = 6X - 7
\]

Now, we will solve for \( X \):

1. Subtract \( 2X \) from both sides:
\[
5 = 4X - 7
\]

2. Add \( 7 \) to both sides:
\[
12 = 4X
\]

3. Divide by \( 4 \):
\[
X = 3
\]

Now that we have the value of \( X \), we can find DE (or FE):

\[
DE = 2X + 5 = 2(3) + 5 = 6 + 5 = 11
\]

Thus, the length of DE is:

\[
\boxed{11}
\]