+1450 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!
+128408 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 :
