# 1. Option 1

On the sheet, three rectangles A, B, and C are drawn.

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-01.jpg?height=232&width=658&top_left_y=1450&top_left_x=728)

A
5
B

Rectangles A and B have the same width, and rectangles B and C have the same length (width - top to bottom, length - left to right). The length of rectangle B is 2 cm longer than the length of rectangle A, and the area of B is 22 cm² larger than the area of rectangle A. The width of rectangle C is 4 cm less than the width of rectangle B, and the area of C is 40 cm² less than the area of B. Find the area of rectangle A in square centimeters.
Answer: 88.

Solution: Let rectangle A have a length of $a$ cm and a width of $b$ cm. If the length is increased by 2 cm, the area will increase by $2 b$ cm $^{2}$. Therefore, $2 b=22, b=11$. The area of rectangle B is 40 cm $^{2}$ less than that of rectangle B, so the length of rectangle B is $40: 4=10$ cm. Therefore, the length of rectangle A is $a=10-2=8$ cm. Its area is $a b=88$ cm $^{2}$.

## Variant 2

Three rectangles A, B, and C are drawn on a sheet.

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=165&width=141&top_left_y=313&top_left_x=732)

A

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=162&width=198&top_left_y=312&top_left_x=888)

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=168&width=279&top_left_y=309&top_left_x=1107)

B

Rectangles A and B have the same width, and rectangles B and C have the same length (width - top to bottom, length - left to right). The length of rectangle B is 3 cm longer than that of rectangle A, and the area of B is 21 cm $^{2}$ larger than that of A. The width of rectangle C is 3 cm less than that of rectangle B, and the area of C is 60 cm $^{2}$ less than that of B. Find the area of rectangle A in square centimeters.

Answer: 119.

## Variant 3

Three rectangles A, B, and C are drawn on a sheet.

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=160&width=138&top_left_y=1286&top_left_x=733)

A

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=152&width=203&top_left_y=1282&top_left_x=885)

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=165&width=266&top_left_y=1278&top_left_x=1119)

B

Rectangles A and B have the same width, and rectangles B and C have the same length (width - top to bottom, length - left to right). The length of rectangle B is 4 cm longer than that of rectangle A, and the area of B is 48 cm $^{2}$ larger than that of A. The width of rectangle C is 3 cm less than that of rectangle B, and the area of C is 39 cm $^{2}$ less than that of B. Find the area of rectangle A in square centimeters.

Answer: 108.

## Variant 4

Three rectangles A, B, and C are drawn on a sheet.

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-02.jpg?height=236&width=658&top_left_y=2235&top_left_x=728)

Rectangles A and B have the same width, and rectangles B and C have the same length (width - top to bottom, length - left to right). The length of rectangle B is 3 cm longer than that of rectangle A, and the area of B is $33$ cm $^{2}$ larger than that of A. The width of rectangle C is 4 cm less than that of rectangle B, and the area of C is 52 cm $^{2}$ less than that of B. Find the area of rectangle A in square centimeters.

Answer: 110.

## Variant 5

Three rectangles A, B, and C are drawn on a sheet.

![](https://cdn.mathpix.com/cropped/2024_05_06_1bd5a25c646ad8e2b536g-03.jpg?height=240&width=660&top_left_y=739&top_left_x=727)

Rectangles A and B have the same width, and rectangles B and C have the same length (width - top to bottom, length - left to right). The length of rectangle B is 4 cm longer than that of rectangle A, and the area of B is 36 cm $^{2}$ larger than that of A. The width of rectangle C is 5 cm less than that of rectangle B, and the area of C is 75 cm $^{2}$ less than that of B. Find the area of rectangle A in square centimeters.

Answer: 99.