The ratio of the length to the width of a rectangle is 14:5. If the length is reduced by 13 cm and the width is increased by 13 cm, the area will be increased by 182 square cm. What is the area of the original rectangle?

Let the original rectangle be 14x in length and 5x in width. The equation (14x-13) × 13-5x × 13 = 182, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 182x-169-65x = 182, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp

How many square centimeters does a rectangle increase by 5cm in length and 4cm in width

Let the length be a and the width be B, and the increased area be (a + 5) x (B + 4) - ab

If the length of a rectangle is reduced by 5cm, the area will be reduced by 10 square centimeters. If the width is increased by 32cm, what is the area of the original rectangle?

If the area of the reduced part is 10 and the length is 5, the width of the rectangle is 10 / 5 = 2 cm. If the area of the increased part is 32 and the width is 4, the length of the rectangle is 32 / 4 = 8 cm. Therefore, the area of the original rectangle is: length * width = 2 * 8 = 16 square cm

For a rectangle, its length is reduced by 1 cm and its width is increased by 3 cm. The square is 21 cm larger than the original rectangle

Length width = 3 + 1 = 4cm
Let the width be x and the length be x + 4
(x+3)²-x(x+4)
=x²+6x+9-x²-4x
=2x+9
=21
2x=12
x=6
Namely
The original rectangle is 10 cm long and 6 cm wide

The length of a rectangle is reduced by 2 cm and the width is increased by 1 / 4. It becomes a square with an area equal to that of the original rectangle. What is the area of the rectangle?
kuaikuai

Let the length and width of the original rectangle be x, y respectively, and the original area be s = XY. The area after the change is s' = (X-2) * (y + Y / 4). If the area before and after the change is unchanged, there will be s = s', (1) after the change, the figure is X-2 = y + Y / 4 ', (2) the length and width of the square are the same

If the width is increased by 12 cm, the rectangle will become a square. What is the area of the original rectangle?

Let the width be X
Length = 3x
3x=x+12
If x = 6, then 3x = 18
So the area is 18x6 = 108 square centimeters
I hope I can help you,

The ratio of the length to the width of a rectangle is 7:3. If the length is reduced by 12 cm and the width is increased by 8 cm, the rectangle will become a square, and the area of the original rectangle will be calculated

（12+8）/（7-3）=5
Length of original rectangle: 7 * 5 = 35 (CM)
The width of the original rectangle: 3 * 5 = 15 (CM)
Area of original rectangle: 35 * 15 = 525 (square centimeter)

Xiao Ming wants to use a square piece of paper with an area of 16cm2 to cut a rectangular piece of paper with an area of 12cm2 along the side, so that the ratio of length to width is 3:2. Can he cut it?

Let the length of the rectangle be 3xcm and the width be 2xcm. According to the meaning of the title, we can get: 6x2 = 12, and the solution is: x = 2, ∵ the area of the square is 16cm2, ∵ the side length of the square is 4cm, ∵ the length of the rectangle is 32 > 4

Reduce one side of a square by 20% and increase the other side by 2 meters to get a rectangle. It has the same area as the original square. What is the area of the square______ Square meters

Let the side length be x meters, 20% X × x = (1-20%) x × 2, & nbsp; & nbsp; 0.2x = 1.6, & nbsp; & nbsp; & nbsp; & nbsp; X = 8; the area is 8 × 8 = 64 (square meters); answer: the area of a square is 64 square meters. So the answer is: 64

The length and width of a rectangle are increased by 20%, and the area of the rectangle is increased by ()
A. 20%B. 40%C. 44%

1.2 × 1.2-1 = 1.44-1 = 0.44 = 44%

The ratio of the length to the width of a rectangle is 14:5. If the length is reduced by 13 cm and the width is increased by 13 cm, the area will be increased by 182 square cm. What is the area of the original rectangle?