Question

cd is the midsegment of trapezoid abgf. ab = 17, fg = ?, cd = 32

Explanation:

Step1: Recall the mid - segment formula for trapezoid

The formula for the mid - segment \(CD\) of a trapezoid \(ABGF\) is \(CD=\frac{AB + FG}{2}\), where \(AB\) and \(FG\) are the lengths of the parallel sides.

Step2: Substitute the known values into the formula

We know that \(AB = 17\) and \(CD=32\). Substituting these values into the formula \(32=\frac{17 + FG}{2}\).

Step3: Solve for \(FG\)

Multiply both sides of the equation by \(2\): \(32\times2=17 + FG\), so \(64 = 17+FG\). Then subtract \(17\) from both sides: \(FG=64 - 17\).

Answer:

\(FG = 47\)