The length of the rectangle is 3 m longer than its width. If the length is reduced by 2 m

The length of the rectangle is 3 m longer than its width. If the length is reduced by 2 m, and the width is increased by 4 m, then the area of the rectangle will increase by 8 m ^ 2. Find the original length and width of the rectangle.

Let’s take the length of the rectangle as x and the width as y.

1. Based on the condition, we compose the equations:

1) x = y + 3,

2) x y + 8 = (x – 2) (y + 4).

2. Simplify the 2nd equation:

x y + 8 = x y + 4 x – 2 y – 8,

x y – x y – 4 x + 2 y = -8 – 8,

– 4 x + 2 y = -16.

3. Substitute the value of x from the 1st equation and find y:

-4 (y + 3) + 2 y = -16,

-4 y – 12 + 2 y = -16,

-2 y = -16 + 12,

-2 y = -4,

y = -4: (-2),

y = 2 m – width.

4. Find the length value, use the 1st equation:

x = y + 3,

x = 2 + 3 = 5 m.

Answer: initial values: length – 5 m, width – 2 m.