2 equal circles in rectangle. if area of rectangle is 50 cm squared, wht is the radius in cm of each circle?
X = Hor. side of recangle.
Y = Ver. side of rectangle.
Ar = X*Y = 50cm^2.
X = 2r1 + 2r2,
X = 2r1 + 2r1 = 4r1.
y = 2r1 = 2r2.
Ar = X*Y = 50,
4r1 * 2r1 = 50,
8r1^2 = 50,
r1^2 = 6.25,
r1 = 2.5cm = r2.
To find the radius of each circle, we first need to determine the dimensions of the rectangle.
Let's assume the length of the rectangle is 'L' and the width is 'W'. We know that the area of a rectangle is calculated by multiplying its length and width, so we have the equation:
Area of Rectangle = Length × Width
Given that the area of the rectangle is 50 cm², we have:
50 = L × W
Now, we need to consider the relationship between the rectangle and the circles. Since the circles are equal, they will have the same radius, denoted by 'r'. We can determine the dimensions of the rectangle using the radius 'r' and the given information.
First, we determine the diameter of one circle, which is twice the radius. So, the diameter is 2r.
To fit two equal circles inside the rectangle, the diameter of each circle must be equal to the width (W) of the rectangle. Therefore, we have:
2r = W
Now that we have an equation for the width of the rectangle in terms of the radius, let's substitute it into the equation for the area of the rectangle:
50 = L × (2r)
To isolate 'r', divide both sides of the equation by 2L:
50 / (2L) = r
Simplifying further:
25 / L = r
So, the radius of each circle is equal to 25 divided by the length of the rectangle (L) in centimeters.