To approach this problem, let's first understand the properties of a rectangle.
1. A rectangle has four sides, with opposite sides being equal in length.
2. The area of a rectangle can be calculated by multiplying the length of one side by the length of an adjacent side.
3. In this case, we are given the area of the rectangle as 30 cm^2.
To determine if it is possible to bend a 20 cm wire into the shape of a rectangle with an area of 30 cm^2, we need to find the dimensions of the rectangle.
Let's assume one side of the rectangle is x cm. Since the opposite sides of a rectangle are equal in length, the other side will also be x cm.
Now, we can use the formula for the area of a rectangle (length × width) to find the dimensions:
Area = length × width
30 cm^2 = x cm × x cm
Simplifying the equation:
30 cm^2 = x^2 cm^2
We can take the square root of both sides to solve for x:
√(30 cm^2) = √(x^2 cm^2)
√(30 cm^2) = x cm
Now, let's calculate the square root of 30 cm^2:
√(30) ≈ 5.48 cm
So, the length of one side of the rectangle would be approximately 5.48 cm.
Since the wire has a length of 20 cm, it is not possible to form a rectangle with sides measuring 5.48 cm using this wire length.
In conclusion, it is not possible to bend a 20 cm wire into the shape of a rectangle with an area of 30 cm^2.