Perimeter of rectangle and a square are equal. Perimeter of the square is 96 cm and breadth of the rectangle is 4 cm less than the side of the square. Then two times the area of the rectangle is
If the rectangle's dimensions are x and y, and the square is side s, then
2x+2y = 4s
2(x+y) = 96
x = s-4
2(x+y) = 2x+2y = 4s = 96
so, s = 24
x = s-4 = 20, so y = 28
2xy = 2*20*28 = 1120
8x+5y=28,2x+3y=11.20
To find the area of the rectangle, we first need to determine the dimensions of the rectangle.
Given that the perimeter of the square is 96 cm, we know that each side of the square is equal. Therefore, the length of one side of the square is 96 cm divided by 4, which gives us 24 cm.
Now, we are told that the breadth of the rectangle is 4 cm less than the side of the square. Since the side of the square is 24 cm, the breadth of the rectangle is 24 cm - 4 cm, which equals 20 cm.
Next, we can calculate the length of the rectangle by using the formula for the perimeter of a rectangle, which is 2 * (length + breadth). We know that the perimeter of the rectangle is equal to the perimeter of the square, so:
2 * (Length of the rectangle + Breadth of the rectangle) = Perimeter of the square
Substituting in the values:
2 * (Length + 20 cm) = 96 cm
Simplifying the equation:
Length + 20 cm = 48 cm
Length = 48 cm - 20 cm
Length = 28 cm
So, the length of the rectangle is 28 cm and the breadth of the rectangle is 20 cm.
To find the area of the rectangle, we use the formula for the area of a rectangle, which is length * breadth:
Area of the rectangle = Length * Breadth
Area of the rectangle = 28 cm * 20 cm
Area of the rectangle = 560 cm^2
Finally, we can calculate two times the area of the rectangle:
Two times the area of the rectangle = 2 * Area of the rectangle
Two times the area of the rectangle = 2 * 560 cm^2
Two times the area of the rectangle = 1120 cm^2
Therefore, two times the area of the rectangle is 1120 cm^2.