# 3. Variant 1

Three rectangles A, B, and C are drawn on the sheet (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-2.jpg?height=327&width=741&top_left_y=1606&top_left_x=692)

Rectangles A and B have the same width, while 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 the length of rectangle A, and the area of B is 12 cm² larger than the area of A. The width of rectangle C is 3 cm larger than the width of rectangle B, and the area of C is 24 cm² larger than the area of B. Find the area of rectangle A in square centimeters.
Answer: 20.

Solution: Let rectangle A have a length of $a$ cm and a width of $b$ cm. If the length is increased by 3 cm, the area increases by $3 b$. Therefore, $3 b=12, b=4$. The area of rectangle B is larger than that of A by $24 \mathrm{~cm}^{2}$, so the length of rectangle B is $24: 3=8$ cm. Therefore, the length of rectangle A is $a=8-3=5$ cm. The area is $a b=20$ cm $^{2}$.

## Variant 2

On a sheet, three rectangles A, B, and C are drawn (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-3.jpg?height=323&width=741&top_left_y=223&top_left_x=689)

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 that of rectangle A, and the area of B is 10 cm ${ }^{2}$ larger than that of A. The width of rectangle C is 2 cm wider than that of rectangle B, and the area of C is 16 cm² larger than that of B. Find the area of rectangle A in square centimeters.

Answer: 30.

## Variant 3

On a sheet, three rectangles A, B, and C are drawn (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-3.jpg?height=320&width=740&top_left_y=1130&top_left_x=690)

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 15 cm² larger than that of A. The width of rectangle C is 2 cm wider than that of rectangle B, and the area of C is 26 cm $^{2}$ larger than that of B. Find the area of rectangle A in square centimeters.

Answer: 50.

## Variant 4

On a sheet, three rectangles A, B, and C are drawn (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-3.jpg?height=326&width=741&top_left_y=2035&top_left_x=689)

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 28 cm² larger than that of A. The width of rectangle C is 3 cm wider than that of rectangle B, and the area of C is 39 cm $^{2}$ larger than that of B. Find the area of rectangle A in square centimeters.

Answer: 63.

## Variant 5

On a sheet, three rectangles A, B, and C are drawn (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-4.jpg?height=171&width=157&top_left_y=630&top_left_x=694)

A

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-4.jpg?height=176&width=225&top_left_y=622&top_left_x=880)

B

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-4.jpg?height=258&width=306&top_left_y=538&top_left_x=1126)

C

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 that of rectangle A, and the area of B is 16 cm $^{2}$ larger than that of A. The width of rectangle C is 4 cm wider than that of rectangle B, and the area of C is 56 cm $^{2}$ larger than that of B. Find the area of rectangle A in square centimeters.

Answer: 96.