Question

ts is the midsegment of trapezoid hjkl. if lk = 19 and ts = 15, find hj. round your answer to nearest tenth, if necessary.

Explanation:

Step1: Recall the midsegment formula for a trapezoid

The midsegment (or median) of a trapezoid is the segment that connects the midpoints of the non - parallel sides. The formula for the length of the midsegment \(TS\) of trapezoid \(HJKL\) is \(TS=\frac{HJ + LK}{2}\), where \(HJ\) and \(LK\) are the lengths of the two parallel sides (bases) of the trapezoid.

Step2: Substitute the known values into the formula

We know that \(TS = 15\) and \(LK=19\). Substituting these values into the formula \(TS=\frac{HJ + LK}{2}\), we get \(15=\frac{HJ + 19}{2}\).

Step3: Solve for \(HJ\)

First, multiply both sides of the equation by 2 to get rid of the denominator: \(15\times2=HJ + 19\), which simplifies to \(30=HJ + 19\). Then, subtract 19 from both sides of the equation: \(HJ=30 - 19\).

Answer:

\(HJ = 11\)