Question

A circle has radius r and a rectangle has length x and width y. the area of the circle is twice the area of the rectangle.express the radius of the circle in terms of x and y

Answer 1

To express the radius r of a circle whose area is twice that of a rectangle with length x and width y, the formula is r = √((2xy) / π).

Step-by-step explanation:

The student is asking to express the radius r of a circle in terms of the length x and width y of a rectangle given that the area of the circle is twice the area of the rectangle. First, we'll determine the area of the rectangle, which is given by the formula A = x × y. Then, we'll write the equation for the area of the circle, which is A = πr². Since the area of the circle is twice the area of the rectangle, we can write 2 × (x × y) = πr².

To solve for r, we'll divide both sides of the equation by π and then take the square root:

πr² = 2xy → r² = (2xy) / π → r = √((2xy) / π).

Therefore, the radius r of the circle can be expressed in terms of x and y using the formula r = √((2xy) / π).