the length of a rectangle exceeds its breadth by 4cm. The length and breadth are increased by 3 cm .The area of the new rectangle will be 81cm square more than the given rectangle .Find the dimensions of the given rectangle?

given original width x and length y,

y = x + 4
(x+3)(y+3) = xy+81

x=10
y=14

check:
14 = 10+4
14*10 = 140
(10+3)(14+3) = 13*17 = 221 = 140+81

Please tell the answer

53

To find the dimensions of the given rectangle, let's analyze the problem step by step.

Let's assume the breadth of the given rectangle is "x" cm. According to the problem, the length of the rectangle exceeds its breadth by 4 cm. Therefore, the length of the rectangle is x + 4 cm.

The area of a rectangle is given by the formula A = length × breadth. So, the area of the given rectangle, which we'll call A1, is:

A1 = (x + 4) × x = x^2 + 4x

According to the problem, both the length and breadth of the rectangle are increased by 3 cm. Therefore, the new length would be (x + 4 + 3) cm = (x + 7) cm, and the new breadth would be (x + 3) cm.

The area of the new rectangle, which we'll call A2, is given as A1 + 81 cm²:

A2 = A1 + 81
A2 = x^2 + 4x + 81

Since the area of the new rectangle (A2) is equal to the length multiplied by the breadth, we can create the following equation:

A2 = (x + 7) × (x + 3)
x^2 + 4x + 81 = x^2 + 10x + 21

Now, let's simplify and solve for x:

x^2 + 4x + 81 - x^2 - 10x - 21 = 0
-6x + 60 = 0
-6x = -60
x = 10

The breadth of the given rectangle is x = 10 cm, and since the length exceeds the breadth by 4 cm, the length is x + 4 = 14 cm.

Therefore, the dimensions of the given rectangle are 14 cm (length) and 10 cm (breadth).