A rectangle is 40 meters longer than its width if its length were increased by 10 meters and its width would be decreased by 5 meters its area would be increased by 190 square meters. Find the dimensions

x(x+40) + 190 = (x-5)(x+40+10)

(x-5)(x+40+10)

Let's let x represent the width of the rectangle.

According to the given information, the length of the rectangle is 40 meters longer than its width, so its length would be x + 40.

If the length were increased by 10 meters, it would become x + 40 + 10 = x + 50.

Similarly, if the width would be decreased by 5 meters, it would become x - 5.

To find the area of the original rectangle, we multiply its length and width: (x + 40)(x).

If the length were increased by 10 meters and the width decreased by 5 meters, the new area would be (x + 50)(x - 5).

According to the problem, the new area would be increased by 190 square meters, so we can set up the equation:

(x + 50)(x - 5) - (x + 40)(x) = 190

To solve this equation, we can multiply out the terms and simplify:

(x^2 + 45x - 250) - (x^2 + 40x) = 190

x^2 + 45x - 250 - x^2 - 40x = 190

Combining like terms:

5x - 250 = 190

Adding 250 to both sides:

5x = 440

Dividing both sides by 5:

x = 88

Therefore, the width of the rectangle is 88 meters.

The length of the rectangle is 40 meters longer than its width, so it would be 88 + 40 = 128 meters.

So, the dimensions of the rectangle are 88 meters (width) and 128 meters (length).

To solve this problem, let's denote the width of the rectangle as "w" and the length as "l".

According to the problem, the length of the rectangle is 40 meters longer than its width, so we can write the equation:
l = w + 40

Now, let's consider what happens if we increase the length by 10 meters and decrease the width by 5 meters. The new length would be (l + 10) and the new width would be (w - 5).

The area of the rectangle is given by the formula:
Area = length * width

Now we need to compare the original area with the new area. According to the problem, the new area is increased by 190 square meters. Mathematically, we can write:
(l + 10) * (w - 5) - l * w = 190

Next, let's substitute the value of l from our first equation into the second equation:
(w + 40 + 10) * (w - 5) - (w + 40) * w = 190

Now we can simplify and solve the equation to find the value of w:
(w + 50) * (w - 5) - (w + 40) * w = 190
(w^2 + 45w - 250) - (w^2 + 40w) = 190
w^2 + 45w - 250 - w^2 - 40w = 190
5w - 250 = 190
5w = 190 + 250
5w = 440
w = 440 / 5
w = 88

Now we can substitute the value of w back into our first equation to find the value of l:
l = w + 40
l = 88 + 40
l = 128

Therefore, the width of the rectangle is 88 meters and the length is 128 meters.