THE LENGTH OF THE RECTANGLE EXCEEDS ITS WIDTH BY 3 CM. IF THE LENGTH AND WIDTH OF EACH INCREASED BY 2 CM, THEN THE AREA OF NEW RECTANGLE WILL BE 70 SQ. CM MORE THAN THAT OF THE GIVEN RECTANGLE. FIND THE LENGTH AND WIDTH OF THE GIVEN RECTANGLE.

L = w + 3

(L+2)(w+2) = 70 + (L)(w)

(w+5)(w+2) = 70 + (w+3)(w)

w^2 + 7 w + 10 = 70 + w^2 + 3 w

4 w - 60 = 0

w = 15
L = w+3 = 18

To find the length and width of the given rectangle, we'll need to set up equations based on the given information.

Let's assume the width of the rectangle is "w" cm. According to the problem, the length exceeds the width by 3 cm, so the length would be "w + 3" cm.

The area of a rectangle is calculated by multiplying its length and width, so the area of the given rectangle would be "w * (w + 3)" square cm.

Now, it is given that if the length and width of the rectangle are increased by 2 cm each, then the area of the new rectangle will be 70 sq. cm more than that of the given rectangle. This can be represented as:

(w + 2) * (w + 3 + 2) = w * (w + 3) + 70

Simplifying the equation:

(w + 2) * (w + 5) = w^2 + 3w + 70

Expanding the left side of the equation:

w^2 + 7w + 10 = w^2 + 3w + 70

Subtracting w^2 + 3w + 70 from both sides:

4w - 60 = 0

Adding 60 to both sides:

4w = 60

Dividing both sides by 4:

w = 15

Therefore, the width of the given rectangle is 15 cm. And since the length exceeds the width by 3 cm, the length would be:

w + 3 = 15 + 3 = 18

So, the length and width of the given rectangle are 18 cm and 15 cm, respectively.