Hello, ExpoSport!

The problem is a bit more complicated than that.

I'll pick the dimensions for my convenience.

Suppose the right triangle has sides: 12, 16, 20 Code:

A o
| *
| *
| *
| *
| * 20
12 | *
| *
| *
| *
| *
| *
C o - - - - - - - - - - - - - - - - - o B
16

Suppose we cut a 1-inch strip from the hypotenuse.

The new (smaller) triangle is *not* 11 by 15 . . .

Code:

A o E
| o
|θ/ *
|/ 1 *
D o *
| * *
| * *
| * *
| * * G
| * o
| * 1/ *
| * / θ *
C o - - - - - - - - - - - o - - - - - o B
F

Let

Then: .

is the width of the strip.

In right triangle

In right triangle

Hence: .

Get the idea?