4. Ira has two identical squares and two identical triangles, from which she formed three figures as shown in the picture, and then calculated the perimeters of these figures. The perimeter of the first figure turned out to be 74, the second - 84, and the third - 82. Find the lengths of the sides of the triangle.

(S. S. Korechkova)
![](https://cdn.mathpix.com/cropped/2024_05_06_89d0c0faea73bc71cf21g-2.jpg?height=226&width=384&top_left_y=1014&top_left_x=1529)
Answer: $5,12,13$.

Solution. Let's denote the sides of the triangle: the shortest side as $k$, the middle side as $c$, and the longest side as $d$. The perimeter of figure №2 differs from figure №1 by two short sides of the triangle, so $k=(84-74): 2=5$. Now we can find the middle side of the triangle from figure №3 - indeed, its perimeter consists of two short sides and six middle sides, so $c=(82-2 k): 6=12$. Finally, now from figure №1 we can find the longest side: $d=(74-4 c): 2=13$.

Criteria. Incorrect answer (except for arithmetic error) and/or partial reasoning leading nowhere -0 points.

Correct answer without any explanation -2 points. Correct answer with verification and/or selection of lengths -3 points.