Question

.The perimeter of retangular field is 32 cm. Keeping the perimeter the same, if thelength is reduced by 2 cm, the area will increase by 12 cm Find the original length​

Answer 1

The original length of the rectangular field is approximately 2.44 cm.

Step-by-step explanation:

The original length of the rectangular field:

Let's assume the original length of the rectangle is x cm. Since the perimeter of the rectangular field is 32 cm, we can set up the equation:

2x + 2y = 32 (where y is the width of the rectangle)

Now, the problem states that if the length is reduced by 2 cm, the area will increase by 12 cm. This can be represented as:

(x - 2)y = xy + 12

To solve this system of equations, we can substitute the value of y from the first equation into the second equation:

(x - 2)(16 - x) = x(16 - x) + 12

Expanding and simplifying the equation gives us:

Simplifying further:

18x - 32 = 12

18x = 44

x = 44/18

x = 22/9

Therefore, the original length of the rectangular field is approximately 2.44 cm.