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Things You'll Need
Instructions
Add the length of all three sides of the triangle to get the perimeter. If the triangle is a right triangle, and you know the length of the base (not the hypotenuse), then the altitude is equal to one of the other sides. Use the Pythagorean theorem to calculate the length of the hypotenuse, and add all the side lengths together. If the triangle is not a right triangle, a good approach is to construct some to determine the unknown lengths of the sides.
Draw a line from the top vertex to the base, extending the base as needed (if you are working with an obtuse triangle) so that the line you draw intersects the base at a 90-degree angle. Your known altitude is now a side of two right triangles. You can use the Pythagorean theorem to determine the unknowns in these triangles based on what you know. The sides of your original triangle are now the hypotenuses of your constructed triangles.
Use trigonometric methods to calculate what you don't know about your triangles from what you know. The altitude of your original triangle is equal to one of the sides of two new right triangles. If you know the angle opposite the side in any right triangle, then dividing the sine function of the angle by your side will give you the length of your hypotenuse, for example. The specific steps you take will vary depending on what information you have.
Don't waste your time trying to determine the perimeter if there is not enough information given. In addition to the altitude, you will need to know either two of the sides, two of the internal angles (which automatically gives you the third angle, because they will sum to 180 degrees), the length of one non-base side and the angle opposite it, or the length of the base and any angle.