In isosceles trapesoid ABCD, AB is congruent to CD. If BC=20, AD=36, ans AB=17, what is the length of the altitude of the trapezoid?

Question

Choices are:

a. 16

b. 12

c. 15

d. 10

 

I already tried 17²+20²=c² to find the third side of the triangle and I got 26.2.

Answer 1

Hi Caleb,

If it's an isosceles trapezoid as you've mentioned, I'm going to presume that BC and AD are the bases.

With that being said, if the top base is 20 and the bottom base is 36, as a trapezoid we can ask the following: how can we make the bottom base equal in length to the top base? How do we get that bottom base of length 36 to become a length of 20?

If we subtract 36 from 20, we get 16. So, if we remove 16 units from the bottom base of the trapezoid, we'll get it to be the same length as the top base. Since this is an isosceles trapezoid, we can take this 16 in equal parts from each side of the bottom base of the trapezoid- so, 8 from one half and 8 from the other. With a length of 8 taken from one side, we actually just found the lower, or short leg of the right triangle with our desired altitude as one of the legs.

Since 17 is the length of AB, or one of the legs of the trapezoid, it's actually the hypotenuse of the right triangle I mentioned above.

Given that, all we need to do is a modified version of the Pythagorean theorem:

172= 8²+a², a=altitude.

this means that a=√(17²-8²) =15.

Thus, 15 is your answer.

Hope this helps, and let me know if you have any questions!