Find a rectangle insde a rotated rectangle that has a different propotion

I have a rectangle, A, of known size, that starts aligned to the x/y axes, and can rotate around its centre point.

For any given angle of rotation, I need to determine the maximum dimensions of a second rectangle, B, that:

- is inscribed inside A
- has a different porportion than A, the propotion of B (Proportion of A not equal to Proportion of B)
- maintains alignment to the x/y axes


So, here A (the black rectangle) has been rotated through 30 degrees (the red rectangle). How do I determine the maximum size of B (the blue rectangle)?

Thanks for any help

Quote:

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Originally Posted by stephencx

I have a rectangle, A, of known size, that starts aligned to the x/y axes, and can rotate around its centre point.

For any given angle of rotation, I need to determine the maximum dimensions of a second rectangle, B, that:

- is inscribed inside A
- has a different porportion than A, the propotion of B (Proportion of A not equal to Proportion of B)
- maintains alignment to the x/y axes


So, here A (the black rectangle) has been rotated through 30 degrees (the red rectangle). How do I determine the maximum size of B (the blue rectangle)?

Thanks for any help

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Could you please provide us with the drawing you are obviously refering to?

Otherwise it's a little bit hard for me to help you.

Attachment 24182