Finding line segments relationships in a isosceles trapezoid

Question

I have a isosceles trapezoid ABCD that has a perimeter of 27.4 inches.  The middle line of the ABCD, EF is 8.62 inches across.  If the top line BC is = to 2 (AB), which is the right side of ABCD, I now need to find AD (the bottom line), AB (the right side), BC (the top line), and CD (the left side).  I know that AB and CD will be equal. I also know that EF is exactly half of BC and AD when added together.  I'm trying to figure out those two angles first but wonder if there is an easier way than just trail and error?

Answer 1

First, write all the given values.

 

Perimeter = 27.4 inches

EF = 8.62 inches

AB = CD because it's an isos.trapezoid

If

BC = 2AB, then BC = 2CD and

BC = AB + CD 

 

Solve for 

AD + BC = EF

      2

AD + BC = 8.62

      2

AD + BC = 17.24

 

(AD + BC) + (AB + CD) = 27.4

17.24 + BC = 27.4

BC = 10.16 inches

 

Substitute the value

AD + 10.16 = 17.24

AD = 7.08 inches

 

BC = 2AB

10.16 = 2AB 

divide both sides by 2

AB = 5.08 inches

CD = 5.08 inches

 

To check your answer, add

AD + BC + AB + CD = 27.4

7.08 + 10.16 + 5.08 + 5.08 = 27.4

27.4 = 27.4