An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. the perimeter of the trapezoid is 58 inches. the average of the bases is 19 inches and the longer base is twice the leg plus 7. find the lengths of the sides.

Perimeter of the trapezoid = a + c + 2b
58 = a + c + 2b

Average of bases = (a + c)/2
19 = (a + c)/2
a + c = 38
Substituting (a + c) into the first equation:

58 = 38 + 2b
b = 10 in

We also know that:
c = 2b + 7
c = 2(10) + 7
c = 27 in

a + 27 = 38
a = 11 in

a = 11 in; b = 10 in; c = 27 in