how to check arithmetic progression of triangle

Question

I solved the problem with the following text:

In a rectangle the sides and the diagonal are an arithmetic progression. Calculate the circumference of the rectangle where the longer side is 44 cm shorter than the diagonal.

I then calculated the progression:

$diagonal = d$

$longer side: a = d-44$

$shorter side: b = d-88$

I then inserted the progression into the formula:

$d^{2}=a^{2}+b^{2}$

substituted the progression:

$d^{2}=(d-44)^{2}+(d-88)^{2}$

and calculated a quadratic equation:

$0=d^{2}-264d+9680$

which gives the two solutions:

$d1=44 cm$

$d2=220 cm$

With the second solution the elements are:

$d = 220, a = 176, b = 132$

My question Is there a good proof of this calculation, or another way of showing that this is the right answer. Is there maybe a good graph that shows this solution?

Answer 1

Let the sides of the rectangle be a(breadth),a+d(length) and a+2d(diagonal). According to the question $$a+2d-a-d=44$$ $$\Rightarrow d=44$$ From here you can get the sides easily.