Question

What is the length of the 2nd base of a trapezoid if the length of one base is 27 and the length of the midsegment is 19?

*Please show all work!

Answer 1

The midsegment of a trapezoid is:

1. parallel to both bases;

2. has length equal to the average of the length of the bases.

If a and b are bases and m - midsegment, then
`m=(a+b)/(2)`. Substitute all given values:

`19=(a+27)/(2) ,\\ \\ 19\cdot 2=a+27,\\ a=38-27, \\ a=11`.

Answer: the length of the second base is 11