Question

For trapezoid GHJK, L and M are the midpoints of the legs. Find KJ

Answer 1

The midsegment of a trapezoid is the segment that joins the midpoints of the legs. It is parallel to the bases. Its length m is equal to the average of the lengths of the bases a and b of the trapezoid:

`\begin{gathered} m=(a+b)/(2) \\ \text{ In this case:} \\ m=25 \\ a=2x+11 \\ b=6x-1 \\ \text{ Replacing the values:} \\ 25=(2x+11+6x-1)/(2) \\ \text{Solve for x:} \\ \text{Multiply both sides by 2:} \\ 50=8x+10 \\ \text{Subtract 10 from both sides:} \\ 40=8x \\ \text{Divide both sides by 8:} \\ (40)/(8)=x \\ x=5 \end{gathered}`

Now, since:

`\begin{gathered} KJ=6x-1 \\ KJ=6(5)-1 \\ KJ=30-1 \\ KJ=29 \end{gathered}`