Humar P.

asked • 03/01/22

What is the length of AD ?

Trapezoid A B C D with shorter base B C at the top and longer base A D at the bottom. Three line segments are drawn inside the figure, all parallel to the bases such that all the segments on the left, A E, E F, F G, and G B are congruent and all the segments on the right, C H, H J, J K, and K D are congruent. The top inside segment, G H, has length 8 x minus 7. The next inside segment, F J, has length 7 x plus 2, and the bottom inside segment, E K, has length 10 x minus 1.What is the length of AD ?

1 Expert Answer

By:

Donald W. answered • 03/01/22

Tutor
5.0 (214)

Experienced and Patient Tutor for Math and Computer Science

See tutors like this
See tutors like this

To solve this problem, we need to use the fact that the length of the median of a trapezoid is the average of the lengths of the two bases. So, let's set up the equation to be:


7x + 2 = (8x - 7 + 10x - 1) / 2


Solving this equation gives us x = 3. Using this value of x, we now know that FJ has length 23 and EK has length 29. Again, using what we know about the median of a trapezoid, we can figure out that AD has length 35.

Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.