An equilateral triangle is a triangle with 3 equal sides.
The perimeter of a triangle is the sum of the lengths of the three sides.
Since the perimeter is 33 and since all three sides are equal in length, each side must be 11.
In an equilateral triangle, not only are the three sides equal, but the three angles are equal, too.
Since the angles of all triangles add up to 180 degrees and since the three angles of an equilateral triangle are equal, each angle must be 60 degrees.
At this point it might help to draw a picture. Draw an equilateral triangle. Then draw an altitude from one vertex to the opposite side.
Since altitudes by definition are perpendicular to the base, the altitude you have drawn splits the equilateral triangle into two right triangles.
Since these right triangles each have a 60 degree angle in it, these right triangles are 30-60-90 right triangles.
The sides of all 30-60-90 right triangles have fixed ratios: The hypotenuse is always twice as long as the side opposite the 30 degree angle. And the side opposite the 60 degree angle is always times the length of the side opposite the 30 degree angle.
The hypotenuse of these right triangles is 11.
So 11 is twice the length of the side opposite the 30 degree angle. That makes the side opposite the 30 degree angle 11/2.
The side opposite the 60 degree angle is times the length of the side opposite the 30 degree angle. So the side opposite the 60 degree angle is .
The side opposite the 60 degree angle is the altitude of the equilateral triangle. So the answer to your problem is or
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