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**+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 :

CPhill
Mar 23, 2018