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Challenge 338: Redha's Triangles

(i) Find all right-angled triangles with sides of integer length for which the perimeter of the triangle is equal to the area of the triangle.

Explain how you know you have found all possible triangles.

(ii) Find the minimum area for a right-angled triangle that has its perimeter equal to its area.

[Note: in (ii), the sides do not have to be of integer length.]

Thanks to Redha, Y12, for this problem