A parallelogram of length 18 inches has two perpendicular lines drawn to its bases as shown. The rectangle has a length of 11 inches and the triangles on the ends are 30° - 60° - 90° right triangles. What is the length of the short side of the parallelogram?

5.5 inches

7 inches

9 inches

14 inches

The short side of the parallelogram is 14 inches.

In a 30-60-90 triangle, we denote the side lengths as t, 2t, and t√3. The longest side, the hypotenuse, would be 2t; the shortest side, the side opposite the 30° angle, would be t; and the side opposite the 60° angle would be t√3.

Since the length of the rectangle formed is 11, this means that the remaining piece of that side of the parallelogram, the side of the triangle opposite the 30° angle, is 7.

t = 7

This means that the short side of the parallelogram, which is the hypotenuse of the triangle, would be 2t = 2 (7) = 14.