# 2. Option 1

On a sheet, two rectangles are drawn. It is known that both the length and the width of the second rectangle are 3 cm larger than the length and width of the first rectangle, and the area of the second rectangle is 48 cm ${ }^{2}$ larger than the area of the first rectangle. Find the perimeter of the second rectangle.
Answer: 38.

Solution: Let the first rectangle have a length of $a$ cm and a width of $b$ cm. Then the length of the second rectangle is $a+3$ cm, and the width is $b+3$ cm. From the condition, it follows that $(a+3)(b+3)-a b=48$, then $3(a+b)=39, a+b=13$ and $(a+3)+(b+3)=19$. Therefore, the perimeter is 38 cm.

## Variant 2

On a sheet, two rectangles are drawn. It is known that both the length and the width of the second rectangle are 4 cm greater than the length and width of the first, and the area of the second rectangle is 56 cm $^{2}$ greater than the area of the first. Find the perimeter of the second rectangle.

Answer: 36.

## Variant 3

On a sheet, two rectangles are drawn. It is known that both the length and the width of the second rectangle are 5 cm greater than the length and width of the first, and the area of the second rectangle is $70 \mathrm{~cm}^{2}$ greater than the area of the first. Find the perimeter of the second rectangle.

Answer: 38.

## Variant 4

On a sheet, two rectangles are drawn. It is known that both the length and the width of the second rectangle are 6 cm greater than the length and width of the first, and the area of the second rectangle is 96 cm $^{2}$ greater than the area of the first. Find the perimeter of the second rectangle.

Answer: 44.

## Variant 5

On a sheet, two rectangles are drawn. It is known that both the length and the width of the second rectangle are 7 cm greater than the length and width of the first, and the area of the second rectangle is 98 cm $^{2}$ greater than the area of the first. Find the perimeter of the second rectangle.

Answer: 42.