SOLUTION: Find the height of triangle KLM. They told me the triangle is isosceles, so KL and LM are congruent. The third side, KM, is 42cm. The perimeter is 112cm. From that, I figured ou

Algebra ->  Triangles -> SOLUTION: Find the height of triangle KLM. They told me the triangle is isosceles, so KL and LM are congruent. The third side, KM, is 42cm. The perimeter is 112cm. From that, I figured ou      Log On


   

Question 606387: Find the height of triangle KLM.
They told me the triangle is isosceles, so KL and LM are congruent. The third side, KM, is 42cm. The perimeter is 112cm. From that, I figured out that KL and LM are 35cm. I'm having trouble finding the height... I tried using sine, cosine, and tangent, but I was having trouble. I split the triangle into two and tried to find a sine, cosine, or tangent of the 90 degree angle.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Your assumptions are good so far!
Now drop a line from the vertex L perpendicular to the base (KM)at point Q. This will bisect KM at Q and you will have two congruent right triangles KLQ and MLQ.
The hypotenuse of these right triangles is 35cm and the base of one of the right triangles is 42%2F2+=+21.
Now you can use the Pythgorean theorem to find the height (h).
%2835%29%5E2+=+%2821%29%5E2%2Bh%5E2
1225+=+441%2Bh%5E2 Subtract 441 from both sides.
784+=+h%5E2 Take the square root of both sides.
h+=+28