Thread: Similarity Problem

Hi, in this problem, I'm not sure what the diagram looks like for a start, also I'm not sure how to solve it. I think congruency/similarity is involved.

Let XYZ be a triangle with a right angle at Z. The midpoint of hypotenuse XY is twice as far from side YZ as it is from side XZ. Find the length of side XZ, if XY = 10mm

Hello, BG5965!

If you sketch the diagram, it's quite simple . . .

Let be a triangle with a right angle at
The midpoint of hypotenuse is twice as far from side as it is from side
Find the length of side , if mm

Let = distance from to

Code:

    X *
      |\
      | \
   2d |  \ 5
      |   \
      |  d \  M
      * - - *
      |\    :\
      | \   : \
   2d |  \  :  \ 5
      |   \ :2d \
      |    \:    \
    Z *-----*-----* Y
         d     d

The diagram is filled with congruent right triangles!

Using Pythagorus on

. .


Therefore: .

But with XY = 10, that diagram isn't correct, because although you put d and 2d, when I draw that diagram out with a ruler, it doesn't work!!!

Is there a special way of doing it or do I assume 'not to scale'?

Thanks