Question

in the figure, (overline{lh}) is the midsegment of trapezoid (fgjk). what is the value of (x)?

Explanation:

Step1: Recall the midsegment formula

The formula for the midsegment \(IH\) of a trapezoid \(FGJK\) is \(IH=\frac{FG + KJ}{2}\). Let \(FG=x\), \(IH = 18.6\), and \(KJ=23.6\).

Step2: Substitute values into the formula

Substitute the values into the formula \(18.6=\frac{x + 23.6}{2}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(2\): \(18.6\times2=x + 23.6\), which gives \(37.2=x + 23.6\). Then subtract \(23.6\) from both sides: \(x=37.2-23.6\).

Answer:

\(x = 13.6\)