## Question about determining area of a right triangle, perimeter given, hypotenuse value given in terms of one of the legs.

Hello I have a question about a difficult problem.
The problem states:
Right Triangle- perimeter of 84, and the hypotenuse is 2 greater than the other leg. Find the area of this triangle.
I have tried different methods of solving this problem using Pythagorean Theorem and systems of equations, but cannot find any of the side lengths or the area of the right triangle. I looked for similar problems on StackExchange and around the internet, but could not find anything.
Does anyone know anything that could help find the side lengths of the triangle and the area as well?

Thanks,
William.

## Triangle ABC has a perimeter of 22cm. AB=8 BC=5cm By calculation dedeuce wheter ABC is a right anle triangle

Triangle ABC has a perimeter of 22cm. AB=8 BC=5cm By calculation deduce whether ABC is a right angle triangle

## 1. Introduction.

By-now classical results assert that minimal surfaces (in $$\mathbb R^n$$) are generically “smooth” out of a “small” set.

Question. What are the known regularity results for anisotropic minimal surfaces?

## 2. A more detailed version of the question

For instance, reading a 1972 paper by Bombieri and Giusti I found the following definition:

Definition. A set $$A \subset \mathbb R^n$$ has an oriented boundary of least area if $$\chi_A \in BV(\mathbb R^n)$$ and for every $$g \in BV(\mathbb R^n)$$ with compact support $$K$$ we have $$\tag{1} P(A) := \vert D \chi_A\vert(K) \le \vert D(\chi_A + g)\vert(K)$$ in the sense of measures, being $$\chi_A$$ the characteristic function of the set $$A$$ and $$P(A)$$ the Euclidean perimeter of $$A$$.

The authors say – right after the definition – that “It is known that if $$A$$ has oriented boundary of least area then [..] the boundary is an analytic hypersurface, except possibly for a closed set whose Hausdorff dimension does not exceed $$n-8$$“.

I would like to investigate the analogue of this problem in the anisotropic case. Let me clarify what I mean: let $$f \colon \mathbb R^n \to [0,+\infty)$$ be some good function (say non-negative, convex and positively 1-homogeneous, as usual in Calculus of Variations). We define the anisotropic perimeter of a set $$A$$ (of finite perimeter) by $$P_f(A) := \int_{\partial^e A} f(\nu_A(x))\, d\mathcal H^{n-1}(x)$$ where $$\nu_A$$ is the measure theoretic outer unit normal, $$\partial^e A$$ is the essential boundary and $$\mathcal H^{n-1}$$ is the Hausdorff measure.

What is the analogue of (1) in this case? And are there known regularity results for the solutions to this minimum problem? Can you point out some reference to the literature investigating this problem? Thanks.