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The measure of one of the smaller base angles of an isosceles trapezoid is 60 degrees. The shorter base is 5 inches long and the altitude is 2 sqrt 3 inches long. What is the number of inches in the perimeter of the trapezoid?

 

Thanks!

AnonymousConfusedGuy  Mar 23, 2018
 #1
avatar+87657 
+2

Since this is an isosceles trapezoid.....the non-parallel sides are equal

 

The length of one of the sides, S, is the hypotenuse of a right triangle and is given by

 

sin (60) = 2sqrt(3)  / S

sqrt (3) / 2  =  2sqrt (3) / S

1/2  = 2/S      rearrange  as

S  =  2 / (1/2)   = 4

 

Call the other leg of this triangle, L

And the length of L  can be found as follows :

 

tan (60) = 2sqrt (3) / L

sqrt (3)  = 2sqrt (3)  /L

1  = 2 / L

L  = 2

 

And due to symmetry...the length of the longer base is  5  + 2L  =  9

 

So.....the perimeter  is    5  + 2(4) +  9    =     22  in

 

Here's a pic, ACG :

 

 

cool cool cool

CPhill  Mar 23, 2018
 #2
avatar+1442 
+2

Thanks so much!

AnonymousConfusedGuy  Mar 23, 2018

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