Scaling to match the size

Question

I need a formula to scale a rectangle to fit into a bigger/wider rectangle. I only need to worry on the small rectangle.

The given values only I have are:

Big rectangle:

1. width
2. height (I don't think this is needed)
3. point (i.e x,y)

Small rectangle:

1. width (not really read-only, but still depends)
2. height (read only)
3. scale (I need a formula to compute what value would this be)
4. point

Values are relative to screen pixels.

Answer 1

Find

a = width1 / height1;
b = width2 / height2;

if(a>b)
{
  scale = height1 / height2;
  point.y = y; (from big rectangle)
  point.x = (width1 - width2 * scale) / 2 + x;
}
else
{
  scale = width1 / width2;
  point.x = x; (from big rectangle)
  point.y = (height1 - height2 * scale) / 2 + y;
}

From what I understand, this should do what you wanted.

Edit: See PureW answer for getting the scale only.