An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. The perimeter o

Question

3 years ago

5

An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. The perimeter o

f 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.

Mathematics

1 answer:

garri49 [273] · Answer 1 · 2022-08-11T19:23:02+03:00

garri49 [273]3 years ago

5 0

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