SOLUTION: If the lengths of the bases of an isosceles trapezoid is a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of the diagonal in cm? A)6√10

Algebra ->  Polygons -> SOLUTION: If the lengths of the bases of an isosceles trapezoid is a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of the diagonal in cm? A)6√10      Log On


   

Question 1132048: If the lengths of the bases of an isosceles trapezoid is a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of the diagonal in cm?
A)6√10 B)8√5C)6√3D)10√3E)12√2
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If the lengths of the bases of an isosceles trapezoid is a circle
------------
The lengths cannot be a circle.
Makes no sense.

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the lengths of the bases of an isosceles trapezoid highlight%28cross%28is%29%29 highlight%28cross%28a%29%29 highlight%28cross%28circle%29%29 are 10 cm and 22 cm, and if one of the legs is 10 cm,
then what is the length of the diagonal in cm?
~~~~~~~~~~~~~~~~~~


            As posted,  this text is nonsense.

            I edited it in that unique way to make sense.

            Hope you agree with my editing.

            If so,  then the solution is below. 


Make a sketch.


Let ABCD be the given isosceles trapezoid.
The bases are AB = 22 cm long;  CD = 10 cm;
the lateral sides are AD = BC = 10 cm.


Draw the perpendiculars CE and DF from the vertices C  and D to the base AB.

It is clear that the right-angled triangles ADF  and BCE are congruent.

Then the segments AF and BE have the length  %28AB+-+CD%29%2F2 = %2822-10%29%2F2 = 12%2F2 = 6 cm each.


The height of the trapezoid CE is the leg of the right angled triangle BCE and its length is equal to  sqrt%2810%5E2-6%5E2%29 = sqrt%28100-36%29 = sqrt%2864%29 = 8 cm.


Now from the right-angled triangle AEC you have

    AC = sqrt%28%2810%2B6%29%5E2%2B8%5E2%29 = sqrt%2816%5E2%2B8%5E2%29 = sqrt%28256%2B64%29 = sqrt%28320%29 = sqrt%2816%2A20%29 = 4%2Asqrt%2820%29 = 8%2Asqrt%285%29.


Thus the diagonal of the trapezoid AC is  8%2Asqrt%285%29 cm long.   ANSWER

Solved.   The answer is option  B).