Question

The Length of one side of a rectangle is twice as long as the radius of a circle. You want the area of the rectangle to equal the area of the circle.

How would I solve?

Answer 1

The other side should be equal to circumference.

Answer 2

Why is it (2r) in the 3rd equation and not just r?

Answer 3

@Justanotherguy

Answer 4

I would translate
Length of one side of a rectangle is twice as long as the radius
to
L (length of one side) = (is) 2 * (twice as long) r (the radius)
or
L= 2r

the area of the rectangle is W*L = W*2*r
area of the circle is pi r^2
so we have
2rW= pi r^2

Answer 5

to solve for W in
\[ 2rW= \pi r^2\]
divide both sides by 2r
\[ \frac{2r W}{2r} = \frac{\pi r^2}{2r} \]
and simplify

Answer 6

@Bacon Sorry, I had to leave for some work. And thanks @phi !