a wire of 100cm is bent to from a squre. if a rectangle is formed with same wire having length 5cm more and breadth 5cm less than each side of the square find the difference between the area of the squre and rectangle
square: 25x25 has area 625
rectangle: 20x30 has area 600
To find the difference between the areas of the square and the rectangle, we first need to calculate the side length of the square and the dimensions of the rectangle.
Let's denote the side length of the square as "x". Since the wire is bent to form a square, the perimeter of the square is equal to the length of the wire, which is 100 cm. Since the square has four equal sides, each side has a length of 100 cm divided by 4, which is 25 cm.
Now, for the rectangle, the length is given to be 5 cm more than each side of the square, so it is x + 5 cm. The breadth is 5 cm less than each side of the square, so it is x - 5 cm.
To find the difference between the areas of the square and the rectangle, we need to calculate the areas of both shapes.
The area of a square is given by the formula: Area = side length^2. Therefore, the area of the square is 25 cm * 25 cm = 625 cm².
The area of a rectangle is given by the formula: Area = length * breadth. So, the area of the rectangle is (x + 5 cm) * (x - 5 cm).
Since we know that the perimeter of the square is equal to the length of the wire, we can write an equation to relate the side length of the square to the wire length.
The perimeter of the square is 4 times the side length, so we have 4x = 100 cm.
Dividing both sides by 4, we get x = 25 cm, which is the side length of the square.
Now we can calculate the area of the rectangle using this value of x:
Area of rectangle = (25 cm + 5 cm) * (25 cm - 5 cm) = 30 cm * 20 cm = 600 cm².
Therefore, the difference in area is: 625 cm² - 600 cm² = 25 cm².
Hence, the difference between the area of the square and the rectangle is 25 cm².