Question

In trapezoid JKLM, determine LM.

Answer 1

LM = 12.1

Explanation:

Trapezoid

The midsegment (also known as the median or midline) of a trapezoid is the segment that joins the midpoints of the legs.

The midline is parallel to the bases a and b and its length m is equal to the average of the lengths of the bases of the trapezoid:

`\displaystyle m = (a + b)/(2)`

Since JP and PM are congruent and KQ and QL are congruent, PQ is the midline of the trapezoid JKLM.

We are given the midline m=11.4 and one of the bases a=10.7. We can find the other base by solving for b:

b = 2m - a

b = 2*11.4 - 10.7

b = 12.1

LM = 12.1