# Task № 6.1

## Condition:

Anya, Tanya, and Vanya had identical cardboard squares with a side of 16 cm. Each of them cut off two rectangles from their square, as shown in the figure, and all 6 rectangles are the same. The perimeter of Anya's figure is 88 cm, and the perimeter of Vanya's figure is 82 cm.

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-21.jpg?height=328&width=332&top_left_y=567&top_left_x=248)

Anya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-21.jpg?height=343&width=343&top_left_y=568&top_left_x=845)

Vanya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-21.jpg?height=343&width=345&top_left_y=565&top_left_x=1438)

Tanya

Find the perimeter of Tanya's figure. Express your answer in centimeters.
Answer: 76

Exact match of the answer - 1 point

## Solution.

The perimeter of the original square is $16 \cdot 4=64 \text{ cm}$. By cutting off 2 rectangles, Anya increased the perimeter of the figure by 4 larger sides of the rectangles, specifically by 88-64=24 cm. The larger side of the rectangle is $24: 4=6$ cm.

Vanya, by cutting off two rectangles, increased the perimeter of the figure by two larger sides of the rectangles and two smaller sides, specifically by 82-64=18 cm, of which 12 cm are the two larger sides, and the remaining 6 cm are the two smaller sides. Thus, the smaller side of the rectangle is 3 cm. Tanya, by cutting off two rectangles, increased the perimeter of the figure by 4 smaller sides of the rectangles, that is, by $3 \cdot 4=12$ cm. The perimeter of the resulting figure is 64+12=76 cm.