Answer
$EF = 1$
$HG = 11$
$CD = 6$
Work Step by Step
According to the trapezoid midsegment theorem, in a quadrilateral that is a trapezoid, the midsegment is parallel to the bases and is half the sum of the base lengths.
Let's set up the equation to find the value of $x$:
$2x + 4 = \frac{1}{2}[(x) + (4x + 7)]$
Evaluate parentheses first:
$2x + 4 = \frac{1}{2}(5x + 7)$
Divide both sides by $\frac{1}{2}$ to get rid of the fraction.
$2(2x + 4) = 5x + 7$
$4x + 8 = 5x + 7$
Subtract $5x$ from both sides of the equation to move variable terms to the left side of the equation:
$-x + 8 = 7$
Subtract $8$ from both sides of the equation to move constants to the right side of the equation:
$-x = -1$
Divide both sides by $-1$ to solve for $x$:
$x = 1$
Now we plug $1$ in for $x$
$EF = x$
Let's substitute $1$ for $x$:
$EF = 1$
Let's look at the expression for the longer base:
$HG = 4x + 7$
Substitute $1$ for $x$
$HG = 4(1) + 7$
Multiply first, according to order of operations:
$HG = 4 + 7$
Add to solve:
$HG = 11$
Finally, let's look at the expression for the midsegment:
$CD = 2x + 4$
Substitute $1$ for $x$:
$CD = 2(1) + 4$
Multiply first, according to order of operations:
$CD = 2 + 4$
Add to solve:
$CD = 6$
