SOLUTION: Please help me solve this problem. it has to do with the length of an isosceles trapezoid. 1. An isosceles trapezoid CDEF has bases of lengths 6 and 12 and an altitude of lengt

Algebra ->  Length-and-distance -> SOLUTION: Please help me solve this problem. it has to do with the length of an isosceles trapezoid. 1. An isosceles trapezoid CDEF has bases of lengths 6 and 12 and an altitude of lengt      Log On


   

Question 809780: Please help me solve this problem. it has to do with the length of an isosceles trapezoid.
1. An isosceles trapezoid CDEF has bases of lengths 6 and 12 and an altitude of length 4. find one of the legs CD.

At first i did 6%5E2%2B4%5E2=c%5E2 then i simplified it to 36%2B16=+sqrt%2852%29 I just wanted to know if i was doing the problem correct.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
This is how I picture it.
Altitudes drawn through the ends of the shorter base split the trapezoid into a rectangle with two congruent right triangles, one on each side.
The base of each triangle is %2812-6%29%2F2=3and the altitude is 4 .
Those are the legs of the right triangle.
The hypotenuse, CD, according to the Pythagorean theorem, measures 5 .
I would calculate it as sqrt%283%5E2%2B4%5E2%29=sqrt%289%2B16%29=sqrt%2825%29=5 ,
but I already knew that teachers like 3-4-5 right triangles.
It is easy to remember (3, 4, 5) as the simplest of Pythagorean triples.
I included an extra 3-4-5 right triangle in my drawing because I like them too.
(I like them because (3, 4, 5) is the only Pythagorean triple that I can remember).