Insufficient AltitudeDate: 10/09/2003 at 09:30:33 From: Becky Subject: the perimeter of a triangle The base of a triangle is 1200 ft. The altitude is 500 ft. What is the length of the third side? I am studing for the Praxis I test for my teaching certificate and this was a sample question. I am afraid everything I learned in grammar school has left my brain.... Date: 10/09/2003 at 10:09:37 From: Doctor Edwin Subject: Re: the perimeter of a triagle Hi, Becky. I see two things you should know. First, altitude is not the name for one of the sides of the triangle. If you draw the triangle with one of the lines parallel to the ground (horizontal) and call that the base, then the altitude is the distance from that line to the opposite vertex. Confused? Here, I'll draw one: * *|* * | * * | * * | * *********** Okay, the bottom line is the "base" and the vertical line is the "altitude". So they haven't given you two sides, they've given you one side and one other fact about the triangle. But it's not enough to tell you the perimeter. Here are three triangles with the same altitude and base: * *|* * | * * | * * | * *****|***** * * * * * * * * * *********** * |* * | * * | * * | * * | *********** (I drew the altitude in on the top and bottom triangles, so don't be confused by the extra vertical line--it's not part of the triangle.) The perimeter of the top triangle is smaller than the other two, and the perimeter of the bottom triangle is larger than the other two. Can you see why? The problem is that we don't know any of the angles in your triangle, so we can't tell how the lines are put together. The middle triangle above is a special one, called a right triangle. That square angle at the bottom left is a right angle, 90 degrees. If we know that we're dealing with a right triangle, there are two ways it helps us. First of all, we now know the lengths of TWO of the sides, since one of the sides is the same as the altitude. Second, if we know how big that angle is, we can tell how big the opposite side is. The famous Pythagorean Theorem is a formula that gives us the length of the third side of a trinagle if we know the other two. So my guess would be that either 1) The question is in error. There is no way to calculate the perimeter of a triangle given just the altitude and base. Or 2) The questioners meant to say a right triangle, rather than just a triangle. If it turns out to be (2), and you can't figure out how to use the Pythagorean Theorem to get the length of the third side, write back and I'll help you out with that. Good luck on your teaching certificate! - Doctor Edwin, The Math Forum http://mathforum.org/dr.math/ |
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