Q:

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

Accepted Solution

A:
1. To solve this exercise you must apply the "Trapezoid midsegment theorem", which says that the length of the midsegment is equal to half the sum of the lengths of the bases of the trapezoid. Therefore, you have:
 
 x=(a+b)/2
 
 "x" is the midsegment (x=19).
 "a" and "b" are the bases (a=27).
 
 2. When you clear the second base "b" from the formula  x=(a+b)/2 and you substitute the values, you obtain: 
 
 x=(a+b)/2
 2x=a+b
 b=2x-a
 b=2(19)-27
 b=38-27
 b=11
 
 What is the length of the 2nd base of a trapezoid?
 
 The answer is: 11