A rectangualar playground is 4 meters longer than it is wide. If the length is increased by 5m, and the width decreased b y 1 m, the area is increased by 15m SQUARED(15M2).Find the original dimensions of the playground.

To find the original dimensions of the playground, let's use algebra.

Let's assume the width of the playground is represented by "x" meters.

According to the given information, the length is 4 meters longer than the width. So, the length is x + 4 meters.

The area of a rectangle is given by the formula: Area = Length * Width.

So, the original area of the playground is x * (x + 4) square meters.

Now, let's consider the changes made to the dimensions:

1. Length increased by 5 meters: The new length becomes (x + 4) + 5 = x + 9 meters.
2. Width decreased by 1 meter: The new width becomes x - 1 meters.

The new area of the playground is (x + 9) * (x - 1) square meters.

According to the given information, the new area is increased by 15 square meters compared to the original area. So, we can set up the equation:

New Area - Original Area = 15

((x + 9) * (x - 1)) - (x * (x + 4)) = 15

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

(x^2 + 8x - 9) - (x^2 + 4x) = 15

x^2 + 8x - 9 - x^2 - 4x = 15

4x - 9 = 15

4x = 24

x = 6

Therefore, the original width of the playground is 6 meters. And since the length is 4 meters longer, the original length is 6 + 4 = 10 meters.

So, the original dimensions of the playground are width = 6 meters and length = 10 meters.