Math CentralQuandaries & Queries


Question from jim:

I think I need a formula. I need to know how far an object will be lifted.
A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side,
if I push down 36 inches on the long side of the beam, how much will the short side move up?

Hi Jim.

The situation you describe is one of similar triangles. If you draw the "before and after" position of the beam and draw the path of the end of the beams, you will see two triangles (pretty close - the ends are actually rounded, but the principle here is the same).

In similar triangles (triangles with different lengths, but the same angles), the ratios of corresponding sides are equal.

Let "h" be the height on the short side, then the ratio between the height and the arm length is h/41.
The ratio between the height and the arm length on the large triangle is 36/246.

But we just said they are equal, so we can set these fractions as equal to each other:

h / 41 = 36 / 246

Can you solve this for h and complete the problem?

Stephen La Rocque

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